Related papers: Stochastic Hyperbolic Systems, Small Perturbations…
Recently, it has been shown in [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43, 2 (2015), 468--527] that there exists a system of stochastic differential equations (SDE) on the time…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…
We study asymptotic error distributions associated with standard approximation scheme for one-dimensional stochastic differential equations driven by fractional Brownian motions. This problem was studied by, for instance, Gradinaru-Nourdin…
In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
We discuss a system of stochastic differential equations with a stiff linear term and additive noise driven by fractional Brownian motions (fBms) with Hurst parameter H>1/2, which arise e. g., from spatial approximations of stochastic…
The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…
We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…
In this paper, we study a conditional distribution dependent stochastic differential equations driven by standard Brownian motion and fractional Brownian motion with Hurst exponent $H>\frac{1}{2}$ simultaneously. First, the existence and…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
We provide a new, concise proof of weak existence and uniqueness of solutions to the stochastic differential equation for the multidimensional skew Brownian motion. We also present an application to Brownian particles with skew-elastic…
This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise…
We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by L\'evy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then,…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…
In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.