Showing papers in "Stochastic Analysis and Applications in 2021"
TL;DR: In this paper, the existence and Hyers-Ulam stability of the almost periodic solution to the fractional differential equation with impulse and fractional Brownian motion under non-local c...
Abstract: The article is devoted to the existence and Hyers-Ulam stability of the almost periodic solution to the fractional differential equation with impulse and fractional Brownian motion under nonlocal c...
75 citations
TL;DR: In this article, the existence of mild solution of non-instantaneous impulsive Hilfer fractional stochastic differential equations (NIHFSDEs) driven by fractional Brownian mappings is analyzed.
Abstract: The aim of this manuscript is to analyze the existence of mild solution of non-instantaneous impulsive Hilfer fractional stochastic differential equations (NIHFSDEs) driven by fractional Brownian m...
23 citations
TL;DR: In this article, the authors investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic differential equations (NSDEs) driven by fractional B...
Abstract: The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic differential equations (NSDEs) driven by fractional B...
18 citations
TL;DR: Multivariate Bessel processes (Xt,k)t≥0 describe interacting particle systems of Calogero-Moser-Sutherland type and are related with β-Hermite and β-Laguerre ensembles.
Abstract: Multivariate Bessel processes (Xt,k)t≥0 describe interacting particle systems of Calogero-Moser-Sutherland type and are related with β-Hermite and β-Laguerre ensembles. They depend on a root system...
16 citations
TL;DR: In this paper, fractional stochastic pseudo-parabolic equations driven by fractional Brownian motion are investigated, and the existence, uniqueness, regularity results for m...
Abstract: In this study, fractional stochastic pseudo-parabolic equations driven by fractional Brownian motion are investigated. This work aims at establishing existence, uniqueness, regularity results for m...
15 citations
TL;DR: In this article, a stochastic SIR model with a saturated incidence rate and saturated treatment function incorporating Levy noise is considered, and the existence of a unique global positivity is proved.
Abstract: In this article, we consider a stochastic SIR model with a saturated incidence rate and saturated treatment function incorporating Levy noise. First, we prove the existence of a unique global posit...
13 citations
TL;DR: In this paper, the evolution of biofilms on surfaces of medical implants, food, machinery, etc. may be modeled via reaction-diffusion partial differential equations, according to Allee effect.
Abstract: The evolution of biofilms on surfaces of medical implants, food, machinery, etc. may be modeled via reaction-diffusion partial differential equations. According to Allee effect, the microbes growth...
11 citations
TL;DR: In this article, the authors formulate ill-posedness of inverse problems of estimation and prediction of Coronavirus Disease 2019 (COVID-19) outbreaks from statistical and mathematical perspectives.
Abstract: We formulate ill-posedness of inverse problems of estimation and prediction of Coronavirus Disease 2019 (COVID-19) outbreaks from statistical and mathematical perspectives. This is by nature a stoc...
9 citations
TL;DR: In this paper, a higher order stochastically perturbed SICA epidemic model for HIV transmission is proposed and sufficient conditions for the existence and uniqueness of an ergodic epidemic model are established.
Abstract: In this paper, we propose and study a higher order stochastically perturbed SICA epidemic model for HIV transmission We obtain sufficient conditions for the existence and uniqueness of an ergodic
8 citations
TL;DR: In this article, the existence, uniqueness, and approximate controllability of mild solutions to second-order stochastic impulsive differential systems were investigated, and they were shown to be controllable.
Abstract: This paper is concerned with existence, uniqueness, and approximate controllability of mild solutions to second-order non-autonomous stochastic impulsive differential systems. The impulsive differe...
8 citations
TL;DR: A new algorithm for the approximation and simulation of twofold iterated stochastic integrals together with the corresponding Levy areas driven by a multidimensional Brownian motion is proposed.
Abstract: A new algorithm for the approximation and simulation of twofold iterated stochastic integrals together with the corresponding Levy areas driven by a multidimensional Brownian motion is proposed. Th...
TL;DR: In this article, the global well-posedness as well as long-term behavior in terms of mean random attractors and invariant measures are investigated for a class of stochastic discrete reaction-diffusion equations.
Abstract: The global well-posedness as well as long-term behavior in terms of mean random attractors and invariant measures are investigated for a class of stochastic discrete reaction-diffusion equations de...
TL;DR: In this article, the authors study zero-sum optimal stopping games associated with perpetual convertible bonds in an extension of the Black-Merton-Scholes model with random dividends under various information flows.
Abstract: We study zero-sum optimal stopping games associated with perpetual convertible bonds in an extension of the Black-Merton-Scholes model with random dividends under various information flows. In this...
TL;DR: In this article, the authors study nonzero-sum stochastic differential games with risk-sensitive discounted cost criteria and establish a Nash equilibria under fairly general conditions on drift term and diffusion coefficients.
Abstract: We study nonzero-sum stochastic differential games with risk-sensitive discounted cost criteria. Under fairly general conditions on drift term and diffusion coefficients, we establish a Nash equili...
TL;DR: In this paper, the authors prove an anticipative sufficient stochastic minimum principle in a jump process setup with initially enlarged filtrations, and apply the result to several portfolio selection problems like mean a...
Abstract: We prove an anticipative sufficient stochastic minimum principle in a jump process setup with initially enlarged filtrations. We apply the result to several portfolio selection problems like mean a...
TL;DR: A theoretical approach for solving time-fractional stochastic Ginzburg-Landau equation with mixed fractional Brownian motion in Hilbert space is elaborated in this article.
Abstract: A theoretical approach for solving time-fractional stochastic Ginzburg–Landau equation with mixed fractional Brownian motion in Hilbert space is elaborated. Initially, the stochastic partial differ...
TL;DR: In this paper, the strong convergence of the Caratheodory numerical scheme for a class of nonlinear McKean-Vlasov stochastic differential equations (MVSDE) was studied under Lipschitz assumptions.
Abstract: We study the strong convergence of the Caratheodory numerical scheme for a class of nonlinear McKean-Vlasov stochastic differential equations (MVSDE). We prove, under Lipschitz assumptions, the con...
TL;DR: In this paper, the shifted Jacobi spectral Galerkin (SJG) method and the shift Jacobi operational matrix (JOM) method were proposed to solve nonlinear stochastic Ito-Volterra integral equations.
Abstract: This article proposes two efficient methods to solve nonlinear stochastic Ito–Volterra integral equations. The shifted Jacobi spectral Galerkin method and shifted Jacobi operational matrix method h...
TL;DR: In this article, an optimal time-consistent proportional reinsurance problem with constraints on the strategies under the mean-variance criterion for an insurer is considered, where it is assumed that the surplus is maximized.
Abstract: This paper considers an optimal time-consistent proportional reinsurance problem with constraints on the strategies under the mean-variance criterion for an insurer. It is assumed that the surplus ...
TL;DR: The strategies on lockdown imposition during the first wave of the pandemic during the second wave crisis are discussed in this article, where the authors show that India, unlike several other countries, has witnessed a greater challenge in overcoming the pand epidemic during the third wave crisis.
Abstract: India, unlike several other countries, has witnessed a greater challenge in overcoming the pandemic during the second wave crisis. The strategies on lockdown imposition during the first wave of the...
TL;DR: In this article, the authors provided a probabilistic SIRD model for the COVID-19 pandemic in Italy, where they allowed the infection, recovery and death rates to be random.
Abstract: We provide a probabilistic SIRD model for the COVID-19 pandemic in Italy, where we allow the infection, recovery and death rates to be random. In particular, the underlying random factor is driven ...
TL;DR: In this article, the authors considered two dimensional stochastic tidal dynamics equations in bounded domains and established the exponential estimates on certain exit times associated with the solution trajectories of the solution.
Abstract: In this work, we consider two dimensional stochastic tidal dynamics equations in bounded domains. We establish the exponential estimates on certain exit times associated with the solution trajector...
TL;DR: In this paper, the estimation of parameters for models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with Gaussian random effects based on discrete observations is discussed.
Abstract: We discuss estimation of parameters for models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with Gaussian random effects based on discrete observations.
TL;DR: In this paper, a Haar wavelet method is proposed for solving linear and nonlinear stochastic Ito-Volterra integral equation (SIVIE) driven by fractional Brownian motion (FBM) with Hurst parameter H.
Abstract: In this paper, a Haar wavelet method is proposed for solving linear and nonlinear stochastic Ito–Volterra integral equation (SIVIE) driven by fractional Brownian motion (FBM) with Hurst parameter H...
TL;DR: In this article, the fractional stochastic integral equation characterized by fractional Brownian motion has been solved by second kind Chebyshev wave, which is a second kind wave wave.
Abstract: In this paper, stochastic integral equations characterized by fractional Brownian motion have been studied. The fractional stochastic integral equation has been solved by second kind Chebyshev wave...
TL;DR: In this paper, the first passage time τ S ( x ) of a one-dimensional continuous stochastic process X ( t ), starting from x ≤ S ( 0 ) through a smooth boundary S(t) is investigated; in particular, diffusions a...
Abstract: The first-passage time τ S ( x ) of a one-dimensional continuous stochastic process X ( t ) , starting from x ≤ S ( 0 ) , through a smooth boundary S(t) is investigated; in particular, diffusions a...
TL;DR: In this article, the authors address the issue of choosing an optimal dynamic reinsurance policy, which is state-dependent, for an insurance company that operates under multiple insurance business lines, and propose an optimal policy for each line.
Abstract: The present paper addresses the issue of choosing an optimal dynamic reinsurance policy, which is state-dependent, for an insurance company that operates under multiple insurance business lines. Fo...
TL;DR: In this paper, the Doob transformation rule is applied to a time-changed Gauss-Markov process and a fractional pseudo-Fokker-Planck equation is given.
Abstract: We consider some time-changed diffusion processes obtained by applying the Doob transformation rule to a time-changed Brownian motion. The time-change is obtained via the inverse of an α-stable subordinator. These processes are specified in terms of time-changed Gauss-Markov processes and fractional time-changed diffusions. A fractional pseudo-Fokker-Planck equation for such processes is given. We investigate their first passage time densities providing a generalized integral equation they satisfy and some transformation rules. First passage time densities for time-changed Brownian motion and Ornstein-Uhlenbeck processes are provided in several forms. Connections with closed form results and numerical evaluations through the level zero are given.
TL;DR: In this paper, two-person zero-sum stochastic games for controlled continuous time Markov chains with risk-sensitive finite-horizon cost criterion were studied, and the transition and cost rates were polynomial.
Abstract: In this paper, we study the two-person zero-sum stochastic games for controlled continuous time Markov chains with risk-sensitive finite-horizon cost criterion. The transition and cost rates are po...
TL;DR: In this paper, the authors considered the Brenier-Schrodinger problem on compact manifolds with boundary, and studied the kinetic property of regular soluti... and showed that the result holds for the case of compact manifold with boundary.
Abstract: We consider the Brenier–Schrodinger problem on compact manifolds with boundary. In the spirit of a work by Arnaudon, Cruzeiro, Leonard, and Zambrini, we study the kinetic property of regular soluti...