Related papers: Approximation analysis for weak solutions of stoch…
The goal of this paper is to clarify when the solutions to stochastic partial differential equations stay close to a given subset of the state space for starting points which are close as well. This includes results for deterministic…
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…
In this paper, we solve stochastic partial differential equations (SPDEs) numerically by using (possibly random) neural networks in the truncated Wiener chaos expansion of their corresponding solution. Moreover, we provide some…
A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of…
In this work we establish weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise, in particular, for the hyperbolic Anderson model. For this class of stochastic partial differential…
We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally…
The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error…
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 derive a strong convergence rate of spatial finite difference approximations for both focusing and defocusing stochastic cubic Schr\"odinger equations driven by a multiplicative $Q$-Wiener process. Beyond the uniform…
In this article, we analyze semi-discrete finite element approximation and full discretization of a fourth-order stochastic pseudo-parabolic equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite…
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…
This paper develops a new efficient scheme for approximations of expectations of the solutions to stochastic differential equations (SDEs). In particular, we present a method for connecting approximate operators based on an asymptotic…
We prove the almost sure weak convergence of a stochastic proximal point method for minimizing a convex integral function in the general nonlinear context of complete geodesic metric spaces of nonpositive curvature (so-called Hadamard…
The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a number of results in the literature that show that Euler-type…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
The aim of this paper is to propose a new method for numerical approximations of the solution of the linear stochastic partial differential equation arising in non-linear filtering problems: the Zaka\"i equation. The approximation scheme is…
The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…
For a mixed stochastic differential equation containing both Wiener process and a H\"older continuous process with exponent $\gamma>1/2$, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of…