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In this paper, we study the stochastic differential equation with singular drift coefficient driven by fractional Brownian motion with Hurst parameter H ∈ (1 2 , 1). We obtain that the optimal convergence rate of the backward Euler method is 1.0. The constant elasticity of variance model and the Aït-Sahalia interest rate model are performed as numerical experiments to validate our theoretical results. [ABSTRACT FROM AUTHOR]

• Nanobody-based dual-mode immunoassay for Ara h 3 was developed with LOD of 6.61 ng/mL. • The dominance of nanobody and B/ N -CDs improved the accuracy of Ara h 3 immunoassay. • The method achieved the assessment of Ara h 3 in peanut contamination foodstuffs. To improve the performance of peanut allergen Ara h 3 detection, depending on boron and nitrogen carbon dots (B/ N -CDs), a nanobody (Nb) mediated dual-mode immunoassay was established, which combines the dominance of colorimetry with ratiometric fluorescence techniques. With the catalysis of Horseradish peroxidase (HRP), the oxidization of o-phenylenediamine (o-PD) in the presence of H 2 O 2 , leading to the production of yellow 2,3-diaminophenolazine (DAP) with an absorption peak at 431 nm. Owing to inner filter effect (IFE), DAP quenched the fluorescence of B/ N -CDs at 426 nm, and it emerged a new emission peak at 549 nm. The fluorescence intensity ratio and absorption intensity can be utilized for quantitative analysis of Ara h 3 concentration. Under optimal conditions, the detection limits were 6.61 and 9.79 ng·mL−1, respectively. The dual-mode immunoassay was assessed containing specificity, stability, reproducibility, and practicability. This method paved the way for sensitive detection of Ara h 3 without background Interference. [ABSTRACT FROM AUTHOR]

The goal of this paper is to construct ergodic estimators for double exponential Ornstein–Uhlenbeck process, where the process is observed at discrete time instants with time step size h. We show the existence and uniqueness of the function equations to determine the estimators for fixed time step size h. Also, we show the strong consistency and the asymptotic normality of the estimators. Furthermore, we propose a simulation method of the double exponential Ornstein–Uhlenbeck process and perform some numerical simulations to demonstrate the effectiveness of the proposed estimators. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of backward doubly stochastic differential equations (BDSDEs for short) with general terminal value and general random generator. Those BDSDEs do not involve any forward diffusion processes. By using the techniques of Malliavin calculus, we are able to establish the L p -Hölder continuity of the solution pair. Then, an implicit numerical scheme for the BDSDE is proposed and the rate of convergence is obtained in the L p -sense. As a by-product, we obtain an explicit representation of the process Y in the solution pair to a linear BDSDE with random coefficients. [ABSTRACT FROM AUTHOR]

This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: ∂ β + ν 2 (− Δ) α ∕ 2 u (t , x) = I t γ ρ (u (t , x)) W ̇ (t , x) , t > 0 , x ∈ R d , where W ̇ is the space–time white noise, α ∈ (0 , 2 ] , β ∈ (0 , 2) , γ ≥ 0 and ν > 0. Fundamental solutions and their properties, in particular the nonnegativity, are derived. The existence and uniqueness of solution together with the moment bounds of the solution are obtained under Dalang's condition: d < 2 α + α β min (2 γ − 1 , 0). In some cases, the initial data can be measures. When β ∈ (0 , 1 ] , we prove the sample path regularity of the solution. [ABSTRACT FROM AUTHOR]

• Our generator is a weighted fractional space-time Brownian field. • And it's not a backward martingale. • The existence, uniqueness and explicit solution pair for Y and Z. • Some kind of sharp Hlder continuity for the solution is obtained. • The Feynman-Kac Formula is established. This paper is concerned with the backward stochastic differential equations whose generator is a weighted fractional Brownian field: Y t = ξ + ∫ t T Y s W (d s , B s) − ∫ t T Z s d B s , 0 ≤ t ≤ T , where W is a (d + 1) -parameter weighted fractional Brownian field of Hurst parameter H = (H 0 , H 1 , ⋯ , H d) , which provide probabilistic interpretations (Feynman-Kac formulas) for certain linear stochastic partial differential equations with colored space-time noise. Conditions on the Hurst parameter H and on the decay rate of the weight are given to ensure the existence and uniqueness of the solution pair. Moreover, the explicit expression for both components Y and Z of the solution pair is given. [ABSTRACT FROM AUTHOR]

Abstract We present an explicit solution triplet (Y , Z , K) to the backward stochastic Volterra integral equation (BSVIE) of linear type, driven by a Brownian motion and a compensated Poisson random measure. The process Y is expressed by an integral whose kernel is explicitly given. The processes Z and K are expressed by Hida–Malliavin derivatives involving Y. [ABSTRACT FROM AUTHOR]

We propose a modified least squares estimator for the drift parameter of the Ornstein–Uhlenbeck process when the observations are available at a discrete instant in a low-frequency level. Unlike in the past literature, this modified least squares estimator is asymptotically unbiased. This estimator is combined with the ergodic theorem to obtain joint estimators ( θ ˆ n , σ ˆ n 2) for both drift and diffusion parameters (θ , σ 2). For any fixed observation time step h > 0 , the strong consistency and joint asymptotic normality of our estimators ( θ ˆ n , σ ˆ n 2) are obtained by using the linear model technology and the Delta method. Surprisingly, this linear model technology is not new but it is used for the first time to our model. It very significantly simplifies the arguments that researchers used in the literature. Numerical results illustrate the asymptotic behavior of the estimators. [ABSTRACT FROM AUTHOR]

This paper studies the weak and strong solutions to the stochastic differential equation d X ( t ) = − 1 2 W ̇ ( X ( t ) ) d t + d B ( t ) , where ( B ( t ) , t ≥ 0 ) is a standard Brownian motion and W ( x ) is a two sided Brownian motion, independent of B . It is shown that the Itô–McKean representation associated with any Brownian motion (independent of W ) is a weak solution to the above equation. It is also shown that there exists a unique strong solution to the equation. Itô calculus for the solution is developed. For dealing with the singularity of drift term ∫ 0 T W ̇ ( X ( t ) ) d t , the main idea is to use the concept of local time together with the polygonal approximation W π . Some new results on the local time of Brownian motion needed in our proof are established. [ABSTRACT FROM AUTHOR]

In this paper, we study the mean square stability of the solution and its stochastic theta scheme for the following stochastic differential equations driven by fractional Brownian motion with Hurst parameter H ∈ (1 2 , 1) : d X (t) = f (t , X (t)) d t + g (t , X (t)) d B H (t). Firstly, we consider the special case when f (t , X) = − λ κ t κ − 1 X and g (t , X) = μ X. Secondly, the stability of the solution and its stochastic theta scheme for nonlinear equations is studied. Due to presence of long memory, even the problem of stability in the mean square sense of the solution has not been well studied, let alone the stability of numerical schemes. A complete new set of techniques to deal with this difficulty are developed. Numerical examples are carried out to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Assuming that a threshold Ornstein–Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. With the sampling time step arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sample size tends to infinity. [ABSTRACT FROM AUTHOR]

We prove a weak rate of convergence of a fully discrete scheme for stochastic Cahn–Hilliard equation with additive noise, where the spectral Galerkin method is used in space and the backward Euler method is used in time. Compared with the Allen–Cahn type stochastic partial differential equation, the error analysis here is much more sophisticated due to the presence of the unbounded operator in front of the nonlinear term. To address such issues, a novel and direct approach has been exploited which does not rely on a Kolmogorov equation but on the integration by parts formula from Malliavin calculus. To the best of our knowledge, the rates of weak convergence are revealed in the stochastic Cahn–Hilliard equation setting for the first time. [ABSTRACT FROM AUTHOR]

In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form (0.1) d Y (t) = − [ α 1 (t) Y (t) + β 1 (t) Z (t) + ∫ R 0 η 1 (t , ζ) K (t , ζ) ν (d ζ) + α 2 (t) E [ Y (t) ] + β 2 (t) E [ Z (t) ] + ∫ R 0 η 2 (t , ζ) E [ K (t , ζ) ] ν (d ζ) + γ (t) ] d t + Z (t) d B (t) + ∫ R 0 K (t , ζ) N ̃ (d t , d ζ) , t ∈ 0 , T , Y (T) = ξ. where (Y , Z , K) is the unknown solution triplet, B is a Brownian motion, N ̃ is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y , Z , K) of such systems. Then we give an explicit formula for the first component Y (t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance. [ABSTRACT FROM AUTHOR]

Abstract: We extend the classical Garsia–Rodemich–Rumsey inequality to the multiparameter situation. The new inequality is applied to obtain some joint Hölder continuity along the rectangles for fractional Brownian fields and for the solution of the stochastic heat equation with additive white noise. [Copyright &y& Elsevier]

Abstract: In this paper, we establish a version of the Feynman–Kac formula for multidimensional stochastic heat equation driven by a general semimartingale. This Feynman–Kac formula is then applied to study some nonlinear stochastic heat equations driven by nonhomogeneous Gaussian noise: first, an explicit expression for the Malliavin derivatives of the solutions is obtained. Based on the representation we obtain the smooth property of the density of the law of the solution. On the other hand, we also obtain the Hölder continuity of the solutions. [Copyright &y& Elsevier]

Abstract: We study the problem of parameter estimation for generalized Ornstein–Uhlenbeck processes driven by -stable noises, observed at discrete time instants. Least squares method is used to obtain an asymptotically consistent estimator. The strong consistency and the rate of convergence of the estimator have been studied. The estimator has a higher order of convergence in the general stable, non-Gaussian case than in the classical Gaussian case. [Copyright &y& Elsevier]

• The first report ever on nanobodies directed against intact S. aureus. • A Nb-mediated immuno-assay avoids false-positive detection of S. aureus. • Development of a sensitive sandwich ELISA against S. aureus. • The potential application to detect intact S. aureus in food matrix. The interaction between conventional immunoglobulins (Igs) and the Ig-binding surface proteins of Staphylococcus aureus (S. aureus) have obstructed the development of immuno-assays to detect these bacteria. The current study aimed to select nanobodies (Nbs) recognizing specifically S. aureus and to establish an immuno-assay to uncover S. aureus contaminations in foods. An alpaca was immunized with an inactivated S. aureus strain followed by the construction of a Nb library from which four target-specific Nbs were retrieved. Subsequently, a sandwich ELISA employing the Nb147 and biotinylated-Nb147 pair to capture and to detect S. aureus , respectively, was established to possess a detection limit of 1.4 × 105 colony forming units (CFU)/mL. The dedicated immuno-assay has been verified by detecting 10 CFU/mL of S. aureus in milk samples after an 8 h-enrichment step. This study provides the basis of an easy, reproducible and effective immuno-assay to screen for S. aureus contaminations in foods. [ABSTRACT FROM AUTHOR]

We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formdX(t)=b(t,X(t),u(t)) dt+σ(t,X(t),u(t)) dB(H)(t),where B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter H=(H1,…,Hm)∈(1/2,1)m. As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion. [Copyright &y& Elsevier]

This paper investigates the finite termination of the optimal solution sequence in parametric optimization as a subproblem of the equilibrium problems. By introducing an augmented mapping on the solution set of the equilibrium problems, we establish the concept of augmented weak sharpness for this set relative to the sequence of optimal solutions in parametric optimization. Augmented weak sharpness is an extension of the concepts of weak sharpness and strongly non-degeneracy. Under the condition that the solution set of the equilibrium problems is augmented weak sharpness, sufficient conditions for the finite termination of the sequence of optimal solutions in parametric optimization are provided. For some special cases of the equilibrium problems (Mathematical Programming (MP), Variational Inequality Problems (VIP), etc.), these results extend the corresponding results under weak sharpness or strongly non-degeneracy conditions in the existing literature. Additionally, they also provide weaker sufficient conditions for the finite termination of many optimization algorithms. [ABSTRACT FROM AUTHOR]

The interaction between diet and gut microbiota plays a critical role in human health. While the conventional in vitro models cannot faithfully recapitulate the intestinal microenvironment including multicellular architectures dynamic, tissue-tissue interfaces, flow, and shear force, which have limited the investigations on interactions between diet components and the gut. Microfluidic chip-based technology promises to overcome the limitations of conventional models by recapitulating tissue- and organ-level physiology and function. This review focuses on summarizing the advances of gut-on-a-chip technologies and their applications for clarifying the interplay mechanisms between diet, microbiota, and host health. Model construction and major components, as well as applications of various models, are summarized and discussed. Gut-on-a-chip could be used as a very promising tool for the evaluation of bioactive components, as well as novel food product development. • The gut-on-a-chip technology has emerged as a very promising in vitro tool. • Deep insight into the diet-microbiota-host crosstalk is possible with the technology. • The advances in the construction of the gut-on-a-chip models are summarized. • The advantages of five classified models are discussed for food nutrition research. [ABSTRACT FROM AUTHOR]

• Water soluble red fluorescent carbon dots had BSA-enhanced fluorescence property. • Fluorescence-wavelength dual-readout POCT was established for detecting BSA. • The carbon dots had hydroxyl radicals-dependent fluorescence quenching property. • Nanobody based fluorescent-photothermal dual-readout immunosensor was established. • The tandem with POCT and immunosensor enable simultaneous detecting BSA and β-LG. Two carbon dots (CDs) (λ Em = 525 nm, G-CDs and λ Em = 640 nm, R-CDs) were synthesized from citric acid and urea. The bovine serum albumin (BSA) responsiveness of the R-CDs was used to develop a "fluorescence-wavelength" label-free point of care testing (POCT) for the detection of the milk quality marker BSA with the detection limit (LOD) of 4.89 μg/mL for fluorescence mode and 3.38 μg/mL for wavelength mode. In addition, R-CDs were found to have hydroxyl radical (·OH)-dependent fluorescence quenching properties, and a "fluorescence-photothermal" immunosensor based on nanobodies was constructed by introducing the fluorescence signal of R-CDs@BSA and the photothermal signal of oxTMB for the detection of β-lactoglobulin (β-LG) with the LOD of 0.034 ng/mL for fluorescence mode and 0.075 ng/mL for photothermal mode. The tandem detection of POCT and immunosensor enables the simultaneous and highly sensitive detection of BSA and β-LG after only simple dilution of less than 5 µL of sample. [ABSTRACT FROM AUTHOR]

In this paper, the active disturbance rejection control (ADRC) approach, an emerging control approach, is applied to output-feedback stabilization for uncertain nonlinear systems disturbed by external stochastic disturbance. Here the disturbance has the form of an uncertain system driven by both Brownian motion and Lévy noises. Firstly, for the sake of estimation for all the states and stochastic disturbance, an efficient extended state observer (ESO) is designed. Then an ESO-based output-feedback control approach and the stability in the mean squared sense are finally developed, respectively. A numerical simulation is also presented to demonstrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we study the exact asymptotic separation rate of two distinct solutions of doubly singular stochastic Volterra integral equations (SVIEs) with two different initial values. The main tool is the Gronwall inequality with doubly singular kernel. For a special linear singular SVIEs, we obtain a bound for the leading coefficient of the asymptotic separation rate for the two distinct solutions which reveals that our asymptotic results are sharp. [ABSTRACT FROM AUTHOR]

• Nanobody-based sandwich ELISA (sELISA) was constructed for detecting β-LG with the LOD of 0.24 ng/mL. • sELISA achieved effectively discrimination of pasteurized milk and UHT milk. • sELISA achieved the assessment of milk or β-LG content in milk-containing and milk-free beverages. The problems of inaccurate detection values of thermal-processed β-lactoglobulin (β-LG) content seriously affect the screening of allergens. A monoclonal antibody (mAb) against β-LG was successfully prepared and a highly sensitive sandwich ELISA (sELISA) was constructed with specific nanobody (Nb) as the capture antibody with detection limit of 0.24 ng/mL. Based on this sELISA, the ability of Nb and mAb to recognize β-LG and β-LG interacting with milk components was explored. Combined with protein structure analysis to elaborate the mechanism of shielding β-LG antigen epitopes during thermal-processing, thus enabling the differentiation between pasteurized and ultra-high temperature sterilized milk, the detection of milk content in milk-containing beverages, and the highly sensitive detection and analysis of β-LG allergens in dairy-free products. The method provides methodological support for identifying the quality of dairy products and reducing the risk of β-LG contamination in dairy-free products. [ABSTRACT FROM AUTHOR]

• Identified the thermal degradation products of creatinine. • Revealed the role of creatinine thermal degradation product in the formation of PhIP. • Verified the radical pathway of PhIP formation by DFT calculations. Creatinine, commonly found in muscle tissue, has been demonstrated as an essential precursor of 2-amino-1-methyl-6-phenylimidazo [4, 5- b ] pyridine (PhIP) in thermally possessed foods. In this current study, formamide and N -methylformamide were identified as the main thermal degradation products of creatinine. The raised production of PhIP and the decreased level of aldol condensation product occurred simultaneously with the increased addition of formamide in the model system of creatinine and phenylacetaldehyde. It was demonstrated that formamide reacted with the aldol condensation product to close the pyridine ring to form PhIP. The radical pathway of PhIP formation was then proposed and verified by density functional theory (DFT) computation and an ion-trap time-of-flight mass spectrometer (IT-TOF-MS). This is the first report of the role of the creatinine thermal degradation product in the pathway of PhIP formation, which could facilitate potential strategies against the inhibition of PhIP formation in thermally processed foods. [ABSTRACT FROM AUTHOR]