Showing papers in "Stochastic Analysis and Applications in 2020"
TL;DR: In this article, the authors consider the two-dimensional viscoelastic fluid flow equations arising from the Oldroyd model for non-Newtonian fluid flows and investigate the well-posedness of such equations.
Abstract: In this work, we consider the two-dimensional viscoelastic fluid flow equations, arising from the Oldroyd model for the non-Newtonian fluid flows. We investigate the well-posedness of such ...
23 citations
TL;DR: The expected information gain is an important quality criterion of Bayesian experimental designs, which measures how much the information entropy about uncertain quantity of interest θ is reduced o... as discussed by the authors, and it is defined as
Abstract: The expected information gain is an important quality criterion of Bayesian experimental designs, which measures how much the information entropy about uncertain quantity of interest θ is reduced o...
22 citations
TL;DR: In this article, the Poisson process of order k (PPoK) time-changed with an independent Levy subordinator and its inverse was studied, which they called TCPPoK-I and TCPPoK-II.
Abstract: In this article, we study the Poisson process of order k (PPoK) time-changed with an independent Levy subordinator and its inverse, which we call, respectively, as TCPPoK-I and TCPPoK-II, t...
18 citations
TL;DR: In this paper, the stability results of higher-order fractional neutral stochastic differential systems with infinite delay driven by Poisson jumps and Rosenblatt process were established and the stability was shown to be stable.
Abstract: In this manuscript, we establish the stability results of higher-order fractional neutral stochastic differential system (FNSDs) with infinite delay driven by Poisson jumps and Rosenblatt process v...
17 citations
TL;DR: In this article, the random dynamics of the N-dimensional stochastic Schrodinger lattice systems with locally Lipschitz diffusion terms driven by locally Linić nonlinear noise was studied.
Abstract: We study the random dynamics of the N-dimensional stochastic Schrodinger lattice systems with locally Lipschitz diffusion terms driven by locally Lipschitz nonlinear noise. We first prove the exist...
17 citations
TL;DR: In this article, the following stochastic heat equation was studied, where L is the generator of a Levy process X in Rd, B is a fractional-colored Gaussian n.
Abstract: In this article, we study the following stochastic heat equation ∂tu(t,x)=Lu(t,x)+Ḃ, u(0,x)=0, 0≤t≤T, x∈Rd, where L is the generator of a Levy process X in Rd, B is a fractional-colored Gaussian n...
15 citations
TL;DR: In this article, the state probabilities of different types of space and time-fractional Poisson processes were derived using z-transform and shown to be similar to the state probability of time fractional poisson processes.
Abstract: In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson proce...
15 citations
TL;DR: In this article, the properties and relationships of commonly employed bounded stochastic processes are investigated with bounded noises, and the relationship between these properties and the properties of bounded noises is investigated.
Abstract: Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated with...
13 citations
TL;DR: In this paper, a stochastic predator-prey model with stage structure for prey is presented, and sufficient conditions for the stage structure are obtained by using the Stochastic Lyapunov Function (SLF) method.
Abstract: In the present paper, we focus on a stochastic predator-prey model with stage structure for prey. Firstly, by using the stochastic Lyapunov function method, we obtain sufficient conditions for the ...
13 citations
TL;DR: In this article, the qualitative analysis of a stochastic two delayed epidemic model incorporating Levy processes with a general nonlinear incidence transmission is considered, and it is shown that the analysis shows that the model is robust to non-linear transmission.
Abstract: In this paper, the qualitative analysis of a stochastic two delayed epidemic model incorporating Levy processes with a general non-linear incidence transmission is considered. Our analysis show tha...
12 citations
TL;DR: In this article, the authors introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance, and the aim is to fin...
Abstract: In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to fin...
TL;DR: In this article, the authors provided conditions implying finite-time blowup of positive weak solutions to the semilinear equation du(t,x)=[Δαu(t.x)+Ku(t.,x)+u1+β(t,x)]dt+μu( t,x),dBtH,u(0,x)=f(x),x∈R ǫd,t≥0, where α∈( 0,2],K ∈R,t ∈ R,t �
Abstract: We provide conditions implying finite-time blowup of positive weak solutions to the semilinear equation du(t,x)=[Δαu(t,x)+Ku(t,x)+u1+β(t,x)]dt+μu(t,x) dBtH,u(0,x)=f(x),x∈R d,t≥0, where α∈(0,2],K∈R,...
TL;DR: In this article, the Lipschitz and W2 estimates for second-order parabolic PDE ∂tu(t,x) = 12Δu( t,x)+f(t,x) on Rd with zero initial data and f satisfying a Ladyzhenskaya-Prod...
Abstract: The goal of this paper is to establish the Lipschitz and W2,∞ estimates for a second-order parabolic PDE ∂tu(t,x)=12Δu(t,x)+f(t,x) on Rd with zero initial data and f satisfying a Ladyzhenskaya–Prod...
TL;DR: In this article, the authors studied the dynamical behavior of a multigroup SIQS epidemic model, which is formulated as a piecewise deterministic Markov process, and provided sufficient conditions for extinction and persistence.
Abstract: In this paper, we study the dynamical behavior of a multigroup SIQS epidemic model, which is formulated as a piecewise deterministic Markov process. Sufficient conditions for extinction and persist...
TL;DR: In this paper, the authors consider a family of non-Volterra quadratic stochastic operators depending on a parameter α and study their trajectory behaviors, and they find all fixed and periodic points for a...
Abstract: In the present paper we consider a family of non-Volterra quadratic stochastic operators depending on a parameter α and study their trajectory behaviors. We find all fixed and periodic points for a...
TL;DR: In this paper, two stochastic predator-prey models with distributed delay and general functional response were studied for the non-autonomous periodic case of the system, by utilizing Khasminskii's t...
Abstract: In this article, we study two stochastic predator-prey models with distributed delay and general functional response. For the nonautonomous periodic case of the system, by utilizing Khasminskii’s t...
TL;DR: In this article, the authors introduce a method for estimating the parameter which governs the tail behavior of the cumulative distribution function of the observed random variable, and they call it In In...
Abstract: We introduce a completely novel method for estimation of the parameter which governs the tail behavior of the cumulative distribution function of the observed random variable. We call it In...
TL;DR: In this paper, the authors derive maximal inequalities for the sub-fractional Brownian motion using comparison theorems for Gaussian processes and show that the maximal inequalities can be obtained for any Gaussian process.
Abstract: We derive some maximal inequalities for the sub-fractional Brownian motion using comparison theorems for Gaussian processes.
TL;DR: In this article, the underlying asset is described by a process with multiple stochastic volatility models, and the model considered in this paper is the same model as the model in this work.
Abstract: In this paper, we consider volatility swap and variance swap when the underlying asset is described by a process with multiple stochastic volatility models. The model considered in this paper is th...
TL;DR: The FIRCEP fills the gap of missing exact method for general kernel satisfying mild regularity conditions in order to develop relation between a class of integrated compound criteria and IMSPE.
Abstract: We discuss the following problem: Given a set of information criteria for optimal designs, the numerical and computational complexity may drastically differ from one criterion to another. A general...
TL;DR: In this paper, the behavior of a particle moving along a d-dimensional lattice and representing a "doubly stochastic" random walk was analyzed. Unlike the classical random walk, the lattice is randomly generated up...
Abstract: We analyze the behavior of a particle moving along a d-dimensional lattice and representing a “doubly stochastic” random walk. Unlike the classical random walk, the lattice is randomly generated up...
TL;DR: A mathematical model for treatment of cancer by using oncolytic virotherapy is proposed and analyzed and it is found that for some set of parameters model system exhibits periodic oscillations.
Abstract: Oncolytic virotherapy is emerging as a promising new method for cancer treatment. In the present study, we propose and analyze a mathematical model for treatment of cancer by using oncolytic viroth...
TL;DR: In this article, the asymptotic properties of the maximum likelihood estimator of the drift parameter in a cusp-type signal driven by a fractional Brownian motion were investigated.
Abstract: We investigate the asymptotic properties of the maximum likelihood estimator of the drift parameter in a cusp-type signal driven by a fractional Brownian motion.
TL;DR: In this paper, the authors investigate statistical operators and an entropy functional for Bernstein stochastic processes associated with hierarchies of forward-backward systems of decoupled deterministic linear parabolic partial di¤erential equations.
Abstract: In this article we de…ne and investigate statistical operators and an entropy functional for Bernstein stochastic processes associated with hierarchies of forward-backward systems of decoupled deterministic linear parabolic partial di¤erential equations. The systems under consideration are de…ned on open bounded domains D R d of Euclidean space where d 2 N + is arbitrary, and are subject to Neumann boundary conditions. We assume that the elliptic part of the parabolic operator in the equations is a self-adjoint Schrodinger operator, bounded from below and with compact resolvent in L 2 (D). The statistical operators we consider are then trace-class operators de…ned from sequences of probabilities associated with the point spectrum of the elliptic part in question, which allow the distinction between pure and mixed processes. We prove in particular that the Bernstein processes of maximal entropy are those for which the associated sequences of probabilities are of Gibbs type. We illustrate our results by considering processes associated with a speci…c hierarchy of forward-backward heat equations de…ned in a two-dimensional disk.
TL;DR: In this article, the authors investigated the multiscale stochastic 3D fractional Leray-α model using the Khasminskii technique and established the strong average principle.
Abstract: This article investigates the multiscale stochastic 3D fractional Leray-α model. By using the Khasminskii technique, we establish the strong average principle for stochastic 3D fractional L...
TL;DR: In this article, an inverse problem for the first-passage place of a one-dimensional diffusion process X(t) with jumps was studied, starting from a random position η∈[a,b].
Abstract: We study an inverse problem for the first-passage place of a one-dimensional diffusion process X(t) (also with jumps), starting from a random position η∈[a,b]. Let be τa,b the first time at which X...
TL;DR: In this paper, the authors explore the stochastic viral infection model and show that this model has a unique global solution, and use the method of Lyapunov function to study the Stochastic asymptotic stabi...
Abstract: In this paper, we explore the stochastic viral infection model and show that this model has a unique global solution. We use the method of Lyapunov function to study the stochastic asymptotic stabi...
TL;DR: In this article, the limiting behavior of non-autonomous stochastic reaction-diffusion equations without uniqueness on unbounded narrow domains was studied and the existence and upper semicontinuity was proved.
Abstract: This paper deals with the limiting behavior of non-autonomous stochastic reaction-diffusion equations without uniqueness on unbounded narrow domains. We prove the existence and upper semicontinuity...
TL;DR: A probabilistic interpretation for the Adomian polynomials (AP’s), which is the main part of the ADM, is provided, both for the one-variable and the multivariable case.
Abstract: The Adomian decomposition method (ADM) is a powerful tool to solve several nonlinear functional equations and a large class of initial/boundary value problems. In this paper, we discuss a probabili...
TL;DR: In this paper, an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations is given.
Abstract: In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential e...