Search

We consider the Schrödinger operator in a bounded domain $ \mathbf{R}^n (n=2,3) $ R n (n = 2 , 3) with Neumann boundary condition. We suppose that this domain contains small deformable inclusions, i.e. regions where the potentials do not have the same values as the exterior medium. Our goal is to construct an asymptotic formula for the case of multiple and simple eigenvalue problems. We find an expansion that highlights the relation between the deformation parameters and the eigenvalues. The problem is devoted to a domain containing a finite number of inhomogeneities. Also, we focus on the interface of a small inclusion. [ABSTRACT FROM AUTHOR]

This article studies an optimal control problem for the financial investment strategy with random incomes. The investment portfolio is simplified to be composed of a risk-free asset and a risky asset. The price of a risky asset is followed by a constant variance elasticity (CEV) model. We consider any correlation coefficient ρ ∈ [ − 1 , 1 ] between the income risk and the risk of risky asset. By applying the Legendre transformation, dual theory, and asymptotic expansion approach, we obtain an asymptotic strategy for the exponential utility function. Numerical examples are presented to illustrate the effects of parameters on the optimal strategy. [ABSTRACT FROM AUTHOR]

AbstractIn this study, we consider the problems of testing for a mean vector and testing the equality of two mean vectors with monotone missing data. We propose new test statistics similar to the simplified Hotelling’s T2-type test statistic for one-sample and two-sample problems under general-step monotone missing data. Approximate upper percentiles of this new statistics are provided by asymptotic expansion along with transformed test statistics based on Bartlett adjustment. Approximate simultaneous confidence intervals for pairwise comparisons among mean vectors are also presented. Furthermore, we investigated the asymptotic behavior of the proposed statistics using a Monte Carlo simulation, and the approximate accuracy of the proposed approximations are provided and discussed. Finally, the numerical power for several statistics is given. [ABSTRACT FROM AUTHOR]

Infinitesimal bendings for classes of two-dimensional surfaces in $ \mathbb {R}^3 $ R 3 are investigated. The techniques used to construct the bending fields include reduction to solvability of Bers–Vekua type equations and systems of differential equations with periodic coefficients. [ABSTRACT FROM AUTHOR]

We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function G (z ; τ). Second, we derive an algorithm for numerically computing the double gamma function and present its complete asymptotic expansion as z → ∞. Third, we derive some new properties, including a new product identity and new representations of the gamma modular forms C (τ) and D (τ). [ABSTRACT FROM AUTHOR]

This work presents an asymptotic method based on angular flux expansion in a Neumann series. The technique is aimed at effective reduction of the memory imprint of numerical methods based on collision probabilities (CPs). The asymptotic method has been implemented in the heterogeneous Cartesian cells of the integro-differential transport solver (IDT). The IDT solves the neutral-particle transport equation by discrete ordinates combined with angular-dependent CP matrices. In lattice depletion calculations, because of the change of isotopic concentration along the burnup, methods based on CP discretization, such as current-coupling CP or the one presented in this paper, would require construction and storage of a set of CP coefficients for any depleted pin cell. When the number of media grows, the performances of the solver are bounded by the memory pressure caused by the growth of coefficients. Application of the asymptotic technique, presented in this paper, transforms by two user's parameters the memory-bound solver in a compute-bound application, where the principal workload is transferred from coefficients to source iterations. In this work, a theoretical study of the method is presented together with two applications to two-dimensional assembly simulations. The effects on self-shielded and depleted materials are highlighted. Preliminary results show an encouraging reduction of memory occupation by a factor 10 without any significant loss of accuracy. [ABSTRACT FROM AUTHOR]

We present sufficient conditions for the asymptotic log-convexity of Apéry-like numbers which satisfy three-term recursions. Our techniques are based on the famous Birkhoff–Adams theorem. [ABSTRACT FROM AUTHOR]

In this paper, testing the equality of two mean vectors is considered when each dataset has a monotone pattern of missing observations. A simplified Hotelling's T2-type test statistic in a two-sample problem under monotone missing data is given. Transformed test statistics of this simplified T2 statistic based on Bartlett adjustment to improve the chi-squared approximation are derived. Furthermore, the accuracy of the approximations is investigated using a Monte Carlo simulation. Finally, the numerical power of the proposed test is presented. [ABSTRACT FROM AUTHOR]

This study proposes an artificial neural network (ANN) based option pricing framework under the SABR (stochastic alpha beta rho) and free boundary SABR volatility models. Unlike previous research, we do not directly apply the ANN technique to train and predict option implied volatilities. Instead, we use the technique to train and predict the differences between the implied volatilities calculated by asymptotic approximation and those computed by Monte Carlo simulation. Since the analytical solution for an option written on an underlying asset price in the SABR model is intractable, approximation techniques are used to derive an approximate closed-form solution in practice. However, these approximation formulas worsen as maturity increases and the underlying asset's volatility is high. The accuracy decreases rapidly in wings, which represents deep in-the-money and out-of-the-money cases. By combining the approximation formulas and ANN framework, our new option pricing method offers the following improvements: (1) the training becomes more robust, and the predictions produce more stable and accurate results: (2) it significantly speeds up the training procedure: and (3) the accuracy and efficiency of approximation are improved in the wings without sacrificing performance. [ABSTRACT FROM AUTHOR]

We consider a Urysohn integral operator K with the kernel of the type of Green's function. For r ≥ 1 , a space of piecewise polynomials of degree ≤ r − 1 with respect to a uniform partition is chosen to be the approximating space, and the projection is chosen to be the orthogonal projection. The iterated Galerkin method is applied to the integral equation x − K (x) = f. It is known that the order of convergence of the iterated Galerkin solution is r + 2 and is 2 r at the partition points. We obtain an asymptotic expansion of the iterated Galerkin solution at the partition points of the above Urysohn integral equation. Richardson extrapolation is used to improve the order of convergence. A numerical example is considered to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an asymptotic expansion for the determinant of the matrix [ Ω n − i + j ] 1 ⩽ i , j ⩽ r , as n → ∞ , where Ω n denotes the volume of the unit ball in R n . [ABSTRACT FROM AUTHOR]

The purpose of this paper is the study of the asymptotic modeling of a linearly thin elastic isotropic membrane shell which is subjected to frictionless contact with a rigid obstacle on part of the boundary. Using the formal asymptotic expansions method, we obtain a two dimensional Signorini membrane shell model, then we justify the result by convergence theorem. [ABSTRACT FROM AUTHOR]

The censored exponential regression model is commonly used for modeling lifetime data. In this paper, we derive a simple matrix formula for the second-order covariance matrix of the maximum likelihood estimators in this class of regression models. The general matrix formula covers many types of censoring commonly encountered in practice. Also, the formula only involves simple operations on matrices and hence is quite suitable for computer implementation. Monte Carlo simulations are provided to show that the second-order covariances can be quite pronounced in small to moderate sample sizes. Additionally, based on the second-order covariance matrix, we propose an alternative Wald statistic to test hypotheses in this class of regression models. Monte Carlo simulation experiments reveal that the alternative Wald test exhibits type I error probability closer to the chosen nominal level. We also present an empirical application for illustrative purposes. [ABSTRACT FROM AUTHOR]

Incorporating information from a prior survey is generally supposed to decrease the estimation risk of the present survey. This paper aims to show how the risk changes by incorporating the information of a prior survey through watching the first and the second-order terms of the asymptotic expansion of the risk. We recognize that the prior information is of some help for risk reduction when we can acquire samples of a sufficient size for both surveys. Interestingly, when the sample size of the present survey is small, the use of the prior survey can increase the risk. In other words, blending information from both surveys can have a negative effect on the risk. Based on these observations, we give some suggestions on whether or not to use the results of the prior survey and the sample size to use in the surveys for a reliable estimation. [ABSTRACT FROM AUTHOR]

We consider the Helmholtz problem with source term in an anisotropic domain of R 3 . The aim of this paper is to investigate the interplay between the geometry and analysis of elliptic equations under small perturbation of domain. The solving of this problem, anisotropic as well as isotropic case, is based on integral equations. We exhibit the Lippmann-Schwinger integral equation in the presence of finite number of anisotropic inclusions of small diameter. We derive some results for convergence estimates. [ABSTRACT FROM AUTHOR]

In this paper, we use asymptotic expansion of the velocity field to reconstruct small deformable droplets (i.e. their forms and locations) immersed in an incompressible Newtonian fluid. Here the fluid motion is assumed to be governed by the non-stationary linear Stokes system. Taking advantage of the smallness of the droplets, our asymptotic formula and identification methods extend those already derived for rigid inhomogeneity and for stationary Stokes system. Our derivations, based on dynamical boundary measurements, are rigorous and proved by involving the notion of viscous moment tensor VMT. The viability of our reconstruction approach is documented by numerical results. [ABSTRACT FROM AUTHOR]

In the paper, the author presents bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function. This result partially confirms one in a series of conjectures on completely monotonic degrees of remainders of asymptotic expansions for the logarithm of the gamma function and for polygamma functions. [ABSTRACT FROM AUTHOR]

A three-dimensional model for a viscous fluid layer separated in two parts by a thin stratified stiff plate is considered. This problem depends on a small parameter ϵ, which is the ratio of the thickness of the plate and that of each of the two parts of the fluid layer. The right-hand side functions are 1-periodic with respect to the tangential variables of the plate. The plate's Young modulus is of order ε − 3 , i.e. it is great, while its density is of order 1. At the solid–fluid interfaces, the velocity and the normal stress are continuous. The variational analysis of this model (including the existence, uniqueness of the solution and its regularity) is provided. An asymptotic expansion of the solution is constructed and justified. The error estimate is established for the partial sums of the asymptotic expansion. The limit problem contains a non-standard interface condition for the Stokes equations. The existence, uniqueness and regularity of its solution are proved. [ABSTRACT FROM AUTHOR]

We consider the nonsteady flow of a micropolar fluid in a thin (or long) curved pipe via rigorous asymptotic analysis. Germano's reference system is employed to describe the pipe's geometry. After writing the governing equations in curvilinear coordinates, we construct the asymptotic expansion up to a second order. Obtained in the explicit form, the asymptotic approximation clearly demonstrates the effects of pipe's distortion, micropolarity and the time derivative. A detailed study of the boundary layers in space is provided as well as the construction of the divergence correction. Finally, a rigorous justification of the proposed effective model is given by proving the error estimates. [ABSTRACT FROM AUTHOR]

We investigate the boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh–Bénard convection with vanishing diffusivity limit. By adopting the multi-scale analysis and the asymptotic expansion methods of singular perturbation theory, we construct an exact approximating solution for the viscous and diffusive Boussinesq system with well-prepared initial data. In addition, we obtain the convergence result of the vanishing diffusivity limit. [ABSTRACT FROM AUTHOR]

A new kind of heavy tail index estimator is proposed by using block order statistics in this paper. The weak consistency of the estimator is derived. The asymptotic expansion and asymptotic normality of the estimator are considered under second order regular variation conditions. Small sample simulations are presented in terms of average mean and average mean squared error to support our findings by comparison with two known heavy tail estimators established by block order statistics method. [ABSTRACT FROM AUTHOR]

In the last two decades, the asymptotic expansion approach has become popular in mathematical finance because it enables us to obtain closed-form approximation formulae for many kinds of options within various kinds of financial models, such as local and stochastic volatility models. In this study, we propose an asymptotic expansion formula for the option price in a constant elasticity of variance model using the asymptotic expansion technique and Fourier analysis. This approach enables us to derive the higher order terms using only algebraic computation. Furthermore, this method enables us to derive not only the price of European options but also the price of options with an early exercise feature, such as Bermudan options and American options. [ABSTRACT FROM AUTHOR]

We explicitly solve the nonlinear PDE that is the continuous limit of dynamic programing equation of the expert prediction problem in finite horizon setting with N = 4 experts. The expert prediction problem is formulated as a zero sum game between a player and an adversary. By showing that the solution is C 2 , we are able to show that the comb strategies, as conjectured by Gravin et al., form an asymptotic Nash equilibrium. We also prove the "Finite vs Geometric regret" conjecture proposed in arXiv:1409.3040 for N = 4, and show that this conjecture in fact follows from the conjecture that the comb strategies are optimal for all N. [ABSTRACT FROM AUTHOR]

We consider the pricing and hedging of American put options under the double Heston model with CIR stochastic interest rate. With an explicit exercise rule American option is approximated by barrier option for which the solution to the partial differential equation is derived by a short-maturity asymptotic expansion. Combining with control variate technique by Fourier-cosine expansion we analytically derive American puts prices and hedging parameters. We also construct a Delta-Vega-Rho hedging strategy of the proposed model for American puts and implement it by Monte Carlo simulation. Numerical results show that the presented pricing method is fast and accurate, the hedging performance of the proposed model is better than that of the BS, Heston and double Heston model. [ABSTRACT FROM AUTHOR]

Multivariate skewness and kurtosis were defined by Mardia. However, the distribution of multivariate normality test statistics based on skewness and kurtosis is only obtainable for large samples. In this paper, we propose a normalizing transformation statistic for Mardia's multivariate kurtosis. The accuracy of the normal approximation of this statistic, i.e. its expectation, variance, skewness, kurtosis, sample error Type I, and power for chosen alternative distributions, was investigated by Monte Carlo simulations for given sizes and dimensions. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to provide an efficient pricing method for single barrier options under the double Heston model. By rewriting the model as a singular and regular perturbed BS model, the double Heston model can separately mimic a fast time-scale and a slow time-scale. With the singular and regular perturbation techniques, we analytically derive the first-order asymptotic expansion of the solution to a barrier option pricing partial differential equation. The convergence and efficiency of the approximate method is verified by Monte Carlo simulation. Numerical results show that the presented asymptotic pricing method is fast and accurate. [ABSTRACT FROM AUTHOR]

In Ferreira and López [Asymptotic expansions of the Hurwitz–Lerch zeta function. J Math Anal Appl. 2004;298(1):210–224], the authors derived an asymptotic expansion of the Lerch's transcendent for large , valid for , and. In this paper, we study the special case not covered in Ferreira and López [Asymptotic expansions of the Hurwitz–Lerch zeta function. J Math Anal Appl. 2004;298(1):210–224], deriving a complete asymptotic expansion of the Lerch's transcendent for z>1 and as goes to infinity. We also show that when a is a positive integer, this expansion is convergent for. As a corollary, we get a full asymptotic expansion for the sum for fixed as. Some numerical results show the accuracy of the approximation. [ABSTRACT FROM AUTHOR]

The initial boundary value problem for the non-steady Stokes system is considered in bounded domains with the boundary having a peak-type singularity (power cusp singularity). The case of the boundary value with a nonzero time-dependent flow rate is studied. The formal asymptotic expansion of the solution near the singular point is constructed. This expansion contains both the outer asymptotic expansion and the boundary-layer-in-time corrector with the 'fast time' variable depending on the distance to the cusp point. The solution of the problem is constructed as the sum of the asymptotic expansion and the term with finite energy. [ABSTRACT FROM AUTHOR]

We propose a new methodology for the calibration of a hybrid credit-equity model to credit default swap (CDS) spreads and survival probabilities. We consider an extended Jump to Default Constant Elasticity of Variance model incorporating stochastic and possibly negative interest rates. Our approach is based on a perturbation technique that provides an explicit asymptotic expansion of the CDS spreads. The robustness and efficiency of the method is confirmed by several calibration tests on real market data. [ABSTRACT FROM AUTHOR]

In this study, the distribution of the simplified Hotelling's statistic for testing the mean vector when a data matrix has a monotone missing pattern is considered. The test statistic is decomposed, and an asymptotic expansion of the null distribution of each term is derived. Using the result, approximations to the upper percentiles of this statistic are derived. Furthermore, transformed test statistics based on the Bartlett adjustment are proposed. Finally, using a Monte Carlo simulation it is shown that the transformed statistics usually perform better than the original statistic with respect to the speed of convergence to the chi-squared limiting distribution. [ABSTRACT FROM AUTHOR]

This work provides a semi-analytic approximation method for decoupled forward-backward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with σ-finite compensators as well as the standard Brownian motions around the small-variance limit of the forward SDE. We provide a semi-analytic solution technique as well as its error estimate for which we only need to solve essentially a system of linear ODEs. In the case of a finite jump measure with a bounded intensity, the method can also handle state-dependent and hence non-Poissonian jumps, which are quite relevant for many practical applications. [ABSTRACT FROM AUTHOR]

This paper focuses on pricing American put options under the double Heston model proposed by Christoffersen et al. By introducing an explicit exercise rule, we obtain the asymptotic expansion of the solution to the partial differential equation for pricing American put options. We calculate American option price by the sum of the European option price and the early exercise premium. The early exercise premium is calculated by the difference between the American and European option prices based on asymptotic expansions. The European option price is obtained by the efficient COS method. Based on the obtained American option price, the double Heston model is calibrated by minimizing the distance between model and market prices, which yields an optimization problem that is solved by a differential evolution algorithm combined with the Matlab function fmincon.m. Numerical results show that the pricing approach is fast and accurate. Empirical results show that the double Heston model has better performance in pricing short-maturity American put options and capturing the volatility term structure of American put options than the Heston model. [ABSTRACT FROM AUTHOR]

In this study, testing the equality of mean vectors in a one-way multivariate analysis of variance (MANOVA) is considered when each dataset has a monotone pattern of missing observations. The likelihood ratio test (LRT) statistic in a one-way MANOVA with monotone missing data is given. Furthermore, the modified test (MT) statistic based on likelihood ratio (LR) and the modified LRT (MLRT) statistic with monotone missing data are proposed using the decomposition of the LR and an asymptotic expansion for each decomposed LR. The accuracy of the approximation for the Chi-square distribution is investigated using a Monte Carlo simulation. Finally, an example is given to illustrate the methods. [ABSTRACT FROM AUTHOR]

We have derived an evolution equation governing the far-field behaviour of small amplitude waves in a non-ideal relaxing gas for planar and converging flow. Asymptotic expansions of the flow variables for small amplitude waves have been used to derive the evolution equation. This equation turns out to be a generalized Burger's equation. The numerical solution of this equation is obtained by using the homotopy analysis method (HAM) proposed by Liao with two different initial conditions. Using the HAM, we have studied the effect of relaxation and nonlinearity. The convergence control parameter enables us to find a good approximate solution for such a complex flow problem. This method also confirms the capabilities and usefulness of convergence control parameter and HAM for complex and highly non-linear problems. [ABSTRACT FROM AUTHOR]

The European sovereign debt crisis, started in the second half of 2011, has posed the problem for asset managers, trades and risk managers to assess sovereign default risk. In the reduced form framework, it is necessary to understand the interrelationship between creditworthiness of a sovereign, its intensity to default and the correlation with the exchange rate between the bond's currency and the currency in which the Credit Default Swap CDS spread are quoted. To do this, we propose a hybrid sovereign risk model in which the intensity of default is based on the jump to default extended constant elasticity variance model. We analyse the differences between the default intensity under the domestic and foreign measure and we compute the default-survival probabilities in the bond's currency measure. We also give an approximation formula to CDS spread obtained by perturbation theory and provide an efficient method to calibrate the model to CDS spread quoted by the market. Finally, we test the model on real market data by several calibration experiments to confirm the robustness of our method. [ABSTRACT FROM AUTHOR]

The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013, Chiarella and Ziveyi considered Christoffersen’s ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast (for example daily) and slow (for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first- and second-order asymptotic expansion formulas. [ABSTRACT FROM PUBLISHER]

The singularities of V-notches in a material whose modulus of elasticity varies as a power function of ther-coordinate are investigated. The eigen-equations are derived by substituting the asymptotic expansions of displacement fields around a notch vertex into the elasticity equilibrium equations. The radial boundary conditions are also presented by a combination of stress singularity orders and eigen-angular functions. The singularity orders and eigen-angular functions can be calculated simultaneously by solving a set of eigen ordinary differential equations with variable coefficients, which are solved by the interpolating matrix method developed by some of the authors before without the iterative process. The accuracy of the proposed method is verified by comparing the present results with the reference ones when the inhomogeneous material is degraded into a homogeneous one. Then, the stress singularities of V-notches in the radially inhomogeneous material under the plane and anti-plane loadings are investigated, respectively. The results show that the stress singularity of a V-notch in the radially inhomogeneous material under the plane loading is more serious than the one under the anti-plane loading. The plane V-notch under the clamped–clamped boundary condition presents the stress singularity at a smaller notch angle α than the one under the free–free boundary condition. The radially inhomogeneous bulgy V-notch even presents singularity. In addition, the stress singularity becomes stronger with the increase of the exponentcin the variation function of the elasticity modulus. [ABSTRACT FROM AUTHOR]

In this paper, we consider an estimation for the unknown parameters of a conditional Gaussian MA(1) model. In the majority of cases, a maximum-likelihood estimator is chosen because the estimator is consistent. However, for small sample sizes the error is large, because the estimator has a bias ofO(n− 1). Therefore, we provide a bias ofO(n− 1) for the maximum-likelihood estimator for the conditional Gaussian MA(1) model. Moreover, we propose new estimators for the unknown parameters of the conditional Gaussian MA(1) model based on the bias ofO(n− 1). We investigate the properties of the bias, as well as the asymptotical variance of the maximum-likelihood estimators for the unknown parameters, by performing some simulations. Finally, we demonstrate the validity of the new estimators through this simulation study. [ABSTRACT FROM PUBLISHER]

We study the asymptotic behavior of the solutions related to a singularly perturbed q-difference-differential problem in the complex domain. The analytic solution can be splitted according to the nature of the equation and its geometry so that both, Gevrey andGevrey asymptotic phenomena are observed and can be distinguished, relating the analytic and the formal solution. The proof leans on a two level novel version of Ramis–Sibuya theorem under Gevrey and q-Gevrey orders. [ABSTRACT FROM PUBLISHER]

The well-known Wilson and Agresti–Coull confidence intervals for a binomial proportionpare centered around a Bayesian estimator. Using this as a starting point, similarities between frequentist confidence intervals for proportions and Bayesian credible intervals based on low-informative priors are studied using asymptotic expansions. A Bayesian motivation for a large class of frequentist confidence intervals is provided. It is shown that the likelihood ratio interval forpapproximates a Bayesian credible interval based on Kerman’s neutral noninformative conjugate prior up toO(n− 1) in the confidence bounds. For the significance level α ≲ 0.317, the Bayesian interval based on the Jeffreys’ prior is then shown to be a compromise between the likelihood ratio and Wilson intervals. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero. For this purpose, we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law. [ABSTRACT FROM PUBLISHER]

This paper develops an asymptotic expansion method for general stochastic differential equations with jumps and their functions. By applying the method, we derive an explicit approximation formula for pricing options on functions of multiple assets under local-stochastic volatility with jump models. Moreover, we present numerical examples for pricing basket options based on the parameters calibrated to the actual market data, which confirms the validity of our method in practice. [ABSTRACT FROM PUBLISHER]

Closed-form likelihood expansion is an important method for econometric assessment of continuous-time models driven by stochastic differential equations based on discretely sampled data. However, practical applications for sophisticated models usually involve significant computational efforts in calculating high-order expansion terms in order to obtain the desirable level of accuracy. We provide new and efficient algorithms for symbolically implementing the closed-form expansion of the transition density. First, combinatorial analysis leads to an alternative expression of the closed-form formula for assembling expansion terms from that currently available in the literature. Second, as the most challenging task and central building block for constructing the expansions, a novel analytical formula for calculating the conditional expectation of iterated Stratonovich integrals is proposed and a new algorithm for converting the conditional expectation of the multiplication of iterated Stratonovich integrals to a linear combination of conditional expectation of iterated Stratonovich integrals is developed. In addition to a procedure for creating expansions for a nonaffine exponential Ornstein–Uhlenbeck stochastic volatility model, we illustrate the computational performance of our method. [ABSTRACT FROM AUTHOR]

The asymptotic approximation of the displacement of a linear elastic beam with prescribed non-homogeneous Dirichlet conditions at an end is constructed. The non-homogeneous Dirichlet conditions considered in this work have the form of rigid displacements. The six values needed to state an auxiliary one-dimensional system are obtained and the error of the approximation is estimated. A numerical example illustrates the high precision of the approximation. [ABSTRACT FROM PUBLISHER]

In this study, a renewal-reward process with a discrete interference of chance is constructed and considered. Under weak conditions, the ergodicity of the processX(t) is proved and exact formulas for the ergodic distribution and its moments are found. Within some assumptions for the discrete interference of chance in general form, two-term asymptotic expansions for all moments of the ergodic distribution are obtained. Additionally, kurtosis coefficient, skewness coefficient, and coefficient of variation of the ergodic distribution are computed. As a special case, a semi-Markovian inventory model of type (s,S) is investigated. [ABSTRACT FROM PUBLISHER]

A three-dimensional model for the interaction of a thin stratified rigid plate and a viscous fluid layer is considered. This problem depends on a small parameterwhich is the ratio of the thickness of the plate and that of the fluid layer. The right-hand side functions are 1-periodic with respect to the tangential variables of the plate. The plate’s Young’s modulus is of order, i.e. it is great, while its density is of order 1. At the solid–fluid interface, the velocity and the normal stress are continuous. The variational analysis of this model (including the existence, uniqueness of the solution and its regularity) is provided. An asymptotic expansion of the solution is constructed and justified. The error estimate is proved for the partial sums of the asymptotic expansion. The limit problem contains a non-standard boundary condition for the Stokes equations. The existence, uniqueness, and regularity of its solution are proved. The asymptotic analysis is applied to the partial asymptotic dimension reduction of the solid phase and the derivation of the asymptotically exact junction conditions between two-dimensional and three-dimensional models of the plate. [ABSTRACT FROM PUBLISHER]

In Bayesian theory, calculating a posterior probability distribution is highly important but typically difficult. Therefore, some methods have been proposed to deal with such problem, among which, the most popular one is the asymptotic expansions of posterior distributions. In this paper, we propose an alternative approach, named a random weighting method, for scaled posterior distributions, and give an ideal convergence rate,o(n( − 1/2)), which serves as the theoretical guarantee for methods of numerical simulations. [ABSTRACT FROM AUTHOR]

We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter ε and we define a perforated domain Ωεobtained by making two small perforations in an open set. Both the size and the distance of the cavities tend to 0 as ε → 0. For ε small, we denote byuεthe solution of a mixed problem for the Laplace equation in Ωε. We describe what happens touεas ε → 0 in terms of real analytic maps and we compute an asymptotic expansion. [ABSTRACT FROM AUTHOR]

A double scale asymptotic method (DSAM) is proposed for vibration modeling of large repetitive sandwich structures with a viscoelastic core. The method decomposes the initial nonlinear vibration problem into two small linear ones. The first one is defined on few basic cells while the second is a differential global amplitude equation with complex coefficients. Their numerical computations permit determination of the damping properties as well as pass and stop bands avoiding the direct computation on the whole structure. Viscoelastic frequency dependent core with fractional and anelastic displacement field models are considered. The resulting nonclassical problems are solved by asymptotic numerical method coupled with automatic differentiation. Based on the presented method, a large reduction of the needed computational time and memory is obtained. The accuracy and efficiency of the proposed method are validated with comparisons to the direct simulations by discretization of the whole structure using asymptotic numerical method coupled with automatic differentiation. [ABSTRACT FROM PUBLISHER]

In 1997, Wilf posed the following elegant infinite product formula as a problem:which contains some of the most important mathematical constants such asπ,e, and the Euler–Mascheroni constantγ. In 2009, Mortini posed the following problem to determineIn this paper, we present the connection between generalized Wilf's and Mortini's problems. We also consider the connection between another infinite product formula and limit relation with several parameters. [ABSTRACT FROM PUBLISHER]