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Prediction of reservoir rock properties, especially permeability distribution is needed for precise simulation of heterogeneous reservoirs. Interwell permeability fields have recently been considered for dynamic simulation using geostatistical models and fractal geometries. The geostatistical models employ experimentally observed variograms to characterize the spatial variability of regionalized variables such as permeability. Fractal models can be useful in assessing the spatial correlation of a property because their variogram can be characterized with a single parameter called the Hurst exponent. In this study, based on core permeability data of each well, Hurst exponent (using R / S analysis) is assigned locally to each well by means of stream lines and as averaged value for interwell spaces. Then, permeability distributions are created using Fractional Brownian Motion (FBM) and Fractional Gaussian Noise (FGN) models by implementing fast Fourier transform (FFT). Through comparison between simulation results of these models, as well as real grid simulation results, the averaged distribution was shown to give better results over a locally assigned fractal distribution. Furthermore, predictions of field pressure using the FGN model were shown to function better than the FBM model for vertical wells. [ABSTRACT FROM AUTHOR]

The dynamic characteristic of macromolecule is mainly subject to the fluctuation of rate constant and this phenomenon is usually considered as dynamic disorder (DD). In order to detect the DD nature in the bio-molecule system more accurately, here we propose a theoretical framework based on the two-dimensional (2D) free-energy landscape including the pulling coordinate and other slow conformational variables. The generalized Langevin equation (GLE) with fractional Gaussian noise (fGn) and the power-law memory kernel are used on this landscape for the research. The transition rate, which depends on both intrinsic barrier height and noise strength ratio, has been analyzed under the condition of external force. The particular discrepancies were investigated between the kinetics of the transitions with and without DD. We find that the discrepancies relied on the barrier height and the noise strength ratio. Taken together, our study illustrates the importance of the DD characteristics, which should be taken into account during the research into the single-molecule pulling experiments. [ABSTRACT FROM AUTHOR]

This paper presents a signal modeling-based new methodology of automatic seizure detection in EEG signals. The proposed method consists of three stages. First, a multirate filterbank structure is proposed that is constructed using the basis vectors of discrete cosine transform. The proposed filterbank decomposes EEG signals into its respective brain rhythms: delta, theta, alpha, beta, and gamma. Second, these brain rhythms are statistically modeled with the class of self-similar Gaussian random processes, namely, fractional Brownian motion and fractional Gaussian noises. The statistics of these processes are modeled using a single parameter called the Hurst exponent. In the last stage, the value of Hurst exponent and autoregressive moving average parameters are used as features to design a binary support vector machine classifier to classify pre-ictal, inter-ictal (epileptic with seizure free interval), and ictal (seizure) EEG segments. The performance of the classifier is assessed via extensive analysis on two widely used data set and is observed to provide good accuracy on both the data set. Thus, this paper proposes a novel signal model for EEG data that best captures the attributes of these signals and hence, allows to boost the classification accuracy of seizure and seizure-free epochs. [ABSTRACT FROM PUBLISHER]

We study the persistence probability for some two-sided, discrete-time Gaussian sequences that are discrete-time analogues of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous time in Molchan (Commun Math Phys 205(1):97–111, 1999) and Molchan (J Stat Phys 167(6):1546–1554, 2017) to a wide class of discrete-time processes. [ABSTRACT FROM AUTHOR]

This paper studies Langevin equation with random damping due to multiplicative noise and its solution. Two types of multiplicative noise, namely the dichotomous noise and fractional Gaussian noise are considered. Their solutions are obtained explicitly, with the expressions of the mean and covariance determined explicitly. Properties of the mean and covariance of the Ornstein–Uhlenbeck process with random damping, in particular the asymptotic behavior, are studied. The effect of the multiplicative noise on the stability property of the resulting processes is investigated. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a new estimator of Hurst exponent based on the combined information of the conventional rescaled range methods. We demonstrate the superiority of the proposed estimator by Monte Carlo simulations, and the applications in estimating the Hurst exponent of daily volatility series in Chinese stock market. Moreover, we indicate the impact of the type of estimator and structural break on the estimating results of Hurst exponent. [ABSTRACT FROM AUTHOR]

A stochastic averaging method of quasi integrable and non-resonant Hamiltonian systems under excitation of fractional Gaussian noise (fGn) with Hurst index 1/2< H <1 is proposed. First, the definitions and the basic properties of fGn and fractional Brownian motion (fBm) are briefly introduced. Then, the averaged fractional stochastic differential equations (SDEs) for the first integrals are derived. The dimension of averaged fractional SDEs is a half of that of the original system. The stationary probability density and statistics of the original system are then obtained approximately from solving the averaged fractional SDEs numerically. Two examples are given to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well. [ABSTRACT FROM AUTHOR]

With the increasing deployment of affordable and sophisticated sensors, multivariate time-series data are increasingly collected. These multivariate time series are often of long memory, the inference of which can be rather complex. We consider the problem of modeling long-memory bivariate time series that are aggregates from an underlying long-memory continuous-time process. We show that, with increasing aggregation, the resulting discrete-time process is approximately a linear transformation of two independent fractional Gaussian noises with the corresponding Hurst parameters equal to those of the underlying continuous-time processes. We use simulations to confirm the good approximation of the limiting model to aggregate data from a continuous-time process. The theoretical and numerical results justify modeling long-memory bivariate aggregate time series by this limiting model. The model parametrization does change drastically in the case of identical Hurst parameters. We derive the likelihood ratio test for testing the equality of the two Hurst parameters, within the framework of Whittle likelihood, and the corresponding maximum likelihood estimators. The limiting properties of the proposed test statistic and of the Whittle likelihood estimation are derived, and their finite sample properties are studied by simulation. The effcacy of the proposed approach is demonstrated with a 2-dimensional robotic positional error time series, which shows that the proposed parsimonious model substantially out- performs a VAR(19) model. [ABSTRACT FROM AUTHOR]

A problem frequently met in engineering hydrology is the forecasting of hydrological variables conditional on their historical observations and the hindcasts and forecasts of a deterministic model. On the contrary, it is a common practice for climatologists to use the output of general circulation models (GCMs) for the prediction of climatic variables despite their inability to quantify the uncertainty of the predictions. Here we apply the well-established Bayesian processor of forecasts (BPF) for forecasting hydroclimatic variables using stochastic models through coupling them with GCMs. We extend the BPF to cases where long-term persistence appears, using the Hurst-Kolmogorov process (HKp, also known as fractional Gaussian noise) and we investigate its properties analytically. We apply the framework to calculate the distributions of the mean annual temperature and precipitation stochastic processes for the time period 2016–2100 in the United States of America conditional on historical observations and the respective output of GCMs. [ABSTRACT FROM PUBLISHER]

In the present paper, for a symmetrical bistable system that is excited by a fractional Gaussian noise, via the examination upon the qualitative changes of the stationary probability densities, the phenomena of the noise induced transition and escape and the stochastic resonance, which is in the sense of that the particles oscillate between the double-well potential, are investigated. For a high noise intensity, the probability density function obtained by Monte Carlo method changes from bimodal to unimodal by decreasing the values of Hurst index H . However, in the low noise intensity regime the transition could not occur for all H . Based on numerical results we demonstrate the fact that the mean first passage time (MFPT) is dependent on the Hurst index H and the noise intensity D , and possesses an exponential form as T ( D , H ) = k 1 ( H ) exp ⁡ ( k 2 ( H ) / D ) . In particular, with a higher noise intensity, T ( D , H ) represents itself as a monotonous increasing function of the MFPT with the increasing H , whereas it exhibits as a non-monotonic function of H in the low noise intensity regime. Finally, nonlinear response theory is applied to investigate the stochastic resonance induced by Hurst index H and noise intensity D , for which we find that only for low noise intensities the stochastic resonance exists via increasing Hurst index which means the effect of noise reduction. This phenomenon is quite different from the one of the classical case. [ABSTRACT FROM AUTHOR]

This article contributes the highlights mainly in two folds. On the one hand, it presents a formula to compute the upper bound of the variance of the correlation periodogram measurement of teletraffic (traffic for short) with long-range dependence (LRD) for a given record length T and a given value of the Hurst parameter H (Theorems 1 and 2). On the other hand, it proposes two formulas for the computation of the variance upper bound of the correlation periodogram measurement of traffic of fractional Gaussian noise (fGn) type and the generalized Cauchy (GC) type, respectively (Corollaries 1 and 2). They may constitute a reference guideline of record length requirement of traffic with LRD. In addition, record length requirement for the correlation periodogram measurement of traffic with either the Schuster type or the Bartlett one is studied and the present results about it show that both types of periodograms may be used for the correlation measurement of traffic with a pre-desired variance bound of correlation estimation. Moreover, real traffic in the Internet Archive by the Special Interest Group on Data Communication under the Association for Computing Machinery of US (ACM SIGCOMM) is analyzed in the case study in this topic. [ABSTRACT FROM AUTHOR]

A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise (fGn) with the Hurst index 1/2 < H < 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion (fBm) are briefly introduced. Then, the averaged fractional stochastic differential equations (SDEs) for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well. [ABSTRACT FROM AUTHOR]

Abstract: This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter α. It is shown that this information measure appropriately describes the complexities of scaling signals and provides further analysis flexibility with the parameter q. In the limit of q → 1, wavelet q-Fisher information reduces to the standard wavelet Fisher information and for q > 2 it reverses its behavior. Experimental results on synthesized fGn signals validates the level-shift detection capabilities of wavelet q-Fisher information. A comparative study also shows that wavelet q-Fisher information locates structural changes in correlated and anti-correlated fGn signals in a way comparable with standard breakpoint location techniques but at a fraction of the time. Finally, the application of this quantifier to H.263 encoded video signals is presented.

This article defines the concept of wavelet-based Fisher’s information measure (wavelet FIM) and develops a closed-form expression of this measure for 1=f α signals. Wavelet Fisher’s information measure characterizes the complexities associated to 1=f α signals and provides a powerful tool for their analysis. Theoretical and experimental studies demonstrate that this quantity is exponentially increasing for α > 1 (non-stationary signals) and almost constant for α < 1 (stationary signals). Potential applications of wavelet FIM are discussed in some detail and its power and robustness for the detection of structural breaks in the mean embedded in stationary fractional Gaussian noise signals studied.

We study persistence probabilities for random walks in correlated Gaussian random environment investigated by Oshanin et al. (Phys Rev Lett, 110:100602, 2013). From the persistence results, we can deduce properties of critical branching processes with offspring sizes geometrically distributed with correlated random parameters. More precisely, we obtain estimates on the tail distribution of its total population size, of its maximum population, and of its extinction time. [ABSTRACT FROM AUTHOR]

The method of detrended fluctuation analysis (DFA) is useful in revealing the extent of long-range dependence, it has successfully been applied to different fields of interest. In this paper we proposed a smoothed detrended fluctuation analysis method based on the principle of wavelet shrinkage. The procedure is illustrated and compared with the DFA method by Monte Carlo simulations on fractional Gaussian noise models. [ABSTRACT FROM AUTHOR]

We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1 . These results allow us to obtain theoretical values of three measures: (i) the recurrence rate ( R E C ) (ii) the percent determinism ( D E T ) and (iii) RP-based estimation of the ε -entropy κ ( ε ) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP. [ABSTRACT FROM AUTHOR]

Emanating from his remarkable characterization of long-term variability in geophysical records in the early 1950s, Hurst’s scientific legacy to hydrology and other disciplines is explored. A statistical explanation of the so-called “Hurst Phenomenon” did not emerge until 1968 when Mandelbrot and co-authors proposed fractional Gaussian noise based on the hypothesis of infinite memory. A vibrant hydrological literature ensued where alternative modelling representations were explored and debated, e.g. ARMA models, the Broken Line model, shifting mean models with no memory, FARIMA models, and Hurst-Kolmogorov dynamics, acknowledging a link with the work of Kolmogorov in 1940. The diffusion of Hurst’s work beyond hydrology is summarized by discipline and citations, showing that he arguably has the largest scientific footprint of any hydrologist in the last century. Its particular relevance to the modelling of long-term climatic variability in the era of climate change is discussed. Links to various long-term modes of variability in the climate system, driven by fluctuations in sea surface temperatures and ocean dynamics, are explored. Several issues related to the Hurst Phenomenon in hydrology remain as a challenge for future research.Editor M. Acreman; Associate editor A. Carsteanu [ABSTRACT FROM AUTHOR]

The variational mode decomposition (VMD) was proposed recently as an alternative to the empirical mode decomposition (EMD). To shed further light on its performance, we analyze the behavior of VMD in the presence of irregular samples, impulsive response, fractional Gaussian noise as well as tones separation. Extensive numerical simulations are conducted to investigate the parameters mentioned in VMD on these filter bank properties. It is found that, unlike EMD, the statistical characterization of the obtained modes reveals a different equivalent filter bank structure, robustness with respect to the nonuniformly sampling and good resolution in spectrum analysis. Moreover, we illustrate the influences of the main parameters on these properties, which provides a guidance on tuning them. Based on these findings, three potential applications in extracting time-varying oscillations, detrending as well as detecting impacts using VMD are presented. [ABSTRACT FROM AUTHOR]

The presence of serial correlation in hydro-meteorological time series often makes the detection of deterministic gradual or abrupt changes with tests such as Mann-Kendall (MK) and Pettitt problematic. In this study we investigate the adverse impact of serial correlation on change point analyses performed by the Pettitt test. Building on methods developed for the MK test, different prewhitening procedures devised to remove the serial correlation are examined, and the effects of the sample size and strength of serial dependence on their performance are tested by Monte Carlo experiments involving the first-order autoregressive [AR(1)] process, fractional Gaussian noise (fGn), and fractionally integrated autoregressive [ARFIMA(1, d,0)] model. Results show that (1) the serial correlation affects the Pettitt test more than tests for slowly varying monotonic trends such as the MK test both for short-range and long-range persistence; (2) the most efficient prewhitening procedure based on AR(1) involves the simultaneous estimation of step change and lag-1 autocorrelation ρ, and bias correction of ρ estimates; (3) as expected, the effectiveness of the prewhitening procedure strongly depends upon the model selected to remove the serial correlation; (4) prewhitening procedures allow for a better control of the type I error resulting in rejection rates reasonably close to the nominal values. As ancillary results, (5) we show the ineffectiveness of the original formulation of the so-called trend-free prewhitening (TFPW) method and provide analytical results supporting a corrected version called TFPWcu; and (6) we propose an improved two-stage bias correction of ρ estimates for AR(1) signals. [ABSTRACT FROM AUTHOR]

This paper introduces a robust voiced/non-voiced (VnV) speech classification method using bivariate empirical mode decomposition (bEMD). Fractional Gaussian noise (fGn) is employed as the reference signal to derive a data adaptive threshold for VnV discrimination. The analyzing speech signal and fGn are combined to generate a complex signal which is decomposed into a finite number of complex-valued intrinsic mode functions (IMFs) by using bEMD. The real and imaginary parts of the IMFs represent the IMFs of observed speech and fGn, respectively. The log-energies of both types of IMFs are calculated. There exist similarities between the IMF log-energy representation of fGn and unvoiced speech signals. Hence, the upper confidence limit from IMF log-energies of fGn is used as data adaptive threshold for VnV classification. If the subband log-energy of speech segment exceeds the threshold, the segment is classified as voiced and unvoiced otherwise. The experimental results show that the proposed algorithm performs better than the recently reported methods without requiring any training data for a wide range of SNRs. [ABSTRACT FROM AUTHOR]

The dynamical map of entanglement, coherence and mixedness in four-qubit maximally entangled GHZ-class state paired with classical channels driven by fractional Gaussian noise is investigated. The qubit-channel coupling is assumed in four distinct ways: common, bipartite, tripartite, and independent local channel-qubit configurations comprising single, double, triple, or independent noisy sources. Using entanglement witness, negativity, purity and von Neumann entropy, except for the independent configuration, we show that indefinite entanglement, coherence, and purity preservation may be simulated in multipartite GHZ-like states. Quantum correlations and purity decrease exponentially in four qubits, and exact fluctuating local field behavior, as well as entanglement sudden death and birth revivals, are completely suppressed. Entanglement, coherence, and purity preservation are affected by noise and the number of independent channels utilized. The Hurst parameter of fractional Gaussian noise was discovered in the four qubits to improve entanglement, coherence and avoid mixedness. [ABSTRACT FROM AUTHOR]

A stochastic averaging method for quasi-non-integrable Hamiltonian systems under excitation of fractional Gaussian noise (fGn) with Hurst index $$1/2

Long-memory processes, in particular fractional Gaussian noise processes, have been applied as models for many phenomena occurring in nature. Non-stationarities, such as trends, mean level-shifts, etc., impact the accuracy of long-memory parameter estimators, giving rise to biases and misinterpretations of the phenomena. In this article, a novel methodology for the detection and location of mean level-shifts in stationary long-memory fractional Gaussian noise (fGn) signals is proposed. It is based on a joint application of the wavelet-Tsallis q-entropy as a preprocessing technique and a peak detection methodology. Extensive simulation experiments in synthesized fGn signals with mean level-shifts confirm that the proposed methodology not only detects, but also locates level-shifts with high accuracy. A comparative study against standard techniques of level-shift detection and location shows that the technique based on wavelet-Tsallis q-entropy outperforms the one based on trees and the Bai and Perron procedure, as well. [ABSTRACT FROM AUTHOR]

A method based on the Bivariate Empirical Mode Decomposition (BEMD) is addressed to facilitate radar scene analysis for cognitive radar, building and expanding upon a previous contribution. The method exploits the response of BEMD to the fractional Gaussian character of coherent sea clutter returns. Second-order properties of the intrinsic mode functions are used to form a null hypothesis, which indicates the absence of target(s) if accepted. Extensive experiments on real-world radar data show that the proposed radar scene analysis procedure leads to significantly enhanced statistical separability for target+clutter and clutter-alone data. The results are judged from an information-theoretic perspective using the Kullback-Leibler distance as well as by visual inspection. [ABSTRACT FROM AUTHOR]

Acoustic energy based localization with wireless sensor networks is an interesting solution to locate sources and targets. For simplicity, localization formulation based on the maximum likelihood (ML) approach considers that the source and noise samples are uncorrelated and represented by a Gaussian distribution. However, the acoustic background noise can severely affect the accuracy of the location estimation. This paper proposes an accurate error estimate in which the correlation of the received signals at each wireless sensor is represented by a Hurst exponent and modeled by a fractional Gaussian noise (fGn). The experimental results show that the proposed solution is more appropriate for the source localization estimation under real acoustic noises and even for highly non-stationary sources. [ABSTRACT FROM PUBLISHER]

The aim of this study is to investigate the effects of sampling rate on Hurst exponents derived from Blood Oxygenation Level Dependent functional Magnetic Resonanse Imaging (BOLD fMRI) resting state time series. fMRI measurements were performed on 2 human subjects and a selection of gel phantoms. From these, Hurst exponents were calculated. It was found that low sampling rates induced non-trivial exponents at sharp material transitions, and that Hurst exponents of human measurements had a strong TR-dependence. The findings are compared to theoretical considerations regarding the fractional Gaussian noise model and resampling, and it is found that the implications are problematic. This result should have a direct influence on the way future studies of low-frequency variation in BOLD fMRI data are conducted, especially if the fractional Gaussian noise model is considered. We recommend either using a different model (examples of such are referenced in the conclusion), or standardizing experimental procedures along an optimal sampling rate.

The discrete-time fractional Gaussian noise (DFGN) has been proven to be a regular process. Therefore, an autoregressive (AR) model of an infinite order can describe DFGN based on Wold and Kolmogorov theorems. A fast estimation algorithm on the Hurst exponent of DFGN or discrete-time fractional Brownian motion (DFBM) has been proposed, but the algorithm did not consider the order selection of AR model. Recently, a Hurst exponent estimator based on an AR model with six existing methods of order selection has been proposed to raise the accuracy of estimating the Hurst exponent. Although the estimation accuracy has been confirmed to be better than the one without order selection, the estimator still requires computing all parameter sets through the Levinson algorithm. In order to lower computational cost, this paper proposes an efficient method of order selection, simply called data induction, which uses simulation data to induce an appropriate threshold of terminating the Levinson algorithm before computing all parameter sets. Experimental results show that the proposed data-induction method has a competitive advantage over six existing methods of order selection in terms of lowering computational cost and raising the accuracy. [ABSTRACT FROM AUTHOR]

We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional Brownian noise. We assume that the classical degree of freedom exposed to the environmental noise is coupled to a quantum degree of freedom of the same system, e.g. its spin, and exploit quantum limited measurements on the spin part to characterize the classical fractional noise. More generally, our approach may be applied to any two-level system subject to dephasing perturbations described by fractional Brownian noise, in order to assess the precision of quantum limited measurements in the characterization of the external noise. In order to assess the performances of quantum probes we evaluate the Bures metric, as well as the Helstrom and the Chernoff bound, and optimize their values over the interaction time. We find that quantum probes may be successfully employed to obtain a reliable characterization of fractional Gaussian process when the coupling with the environment is weak or strong. In the first case decoherence is not much detrimental and for long interaction times the probe acquires information about the environmental parameters without being too much mixed. Conversely, for strong coupling information is quickly impinged on the quantum probe and can be effectively retrieved by measurements performed in the early stage of the evolution. In the intermediate situation, none of the two above effects take place: information is flowing from the environment to the probe too slowly compared to decoherence, and no measurements can be effectively employed to extract it from the quantum probe. The two regimes of weak and strong coupling are defined in terms of a threshold value of the coupling, which itself increases with the fractional dimension. [ABSTRACT FROM AUTHOR]