Related papers: On stochastic finite difference schemes
Considering stochastic partial differential equations of parabolic type with random coefficients in vector-valued H\"older spaces, we obtain a sharp Schauder estimate. As an application, the existence and uniqueness of solution to the…
We consider systems of stochastic evolutionary equations of the $p$-Laplace type. We establish convergence rates for a finite-element based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural…
We define some approximation schemes for different kinds of generalized backward stochastic differential systems, considered in the Markovian framework. We propose a mixed approximation scheme for a decoupled system of forward reflected SDE…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
In this paper we investigate the use of Richardson extrapolation to estimate the convergence rates for numerical solutions to advection problems involving discontinuities. We use modified equation analysis to describe the expectation of the…
In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…
This paper is a survey of methods for solving smooth (strongly) monotone stochastic variational inequalities. To begin with, we give the deterministic foundation from which the stochastic methods eventually evolved. Then we review methods…
Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.
In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…
Finite difference method as a popular numerical method has been widely used to solve fractional diffusion equations. In the general spatial error analyses, an assumption $u\in C^{4}(\bar{\Omega})$ is needed to preserve $\mathcal{O}(h^{2})$…
We obtain existence and uniqueness in L^p, p>1 of the solutions of a backward stochastic differential equations (BSDEs for short) driven by a marked point process, on a bounded interval. We show that the solution of the BSDE can be…
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…
For parabolic stochastic partial differential equations (SPDEs), we show that the numerical methods, including the spatial spectral Galerkin method and further the full discretization via the temporal accelerated exponential Euler method,…
Existence and uniqueness results of fully coupled forward stochastic differential equations without drifts and backward stochastic differential equations in a degenerate case are obtained for an arbitrarily large time duration.
We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Levy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity…
We review recent progress in the study of infinite-dimensional stochastic differential equations with symmetry. This paper contains examples arising from random matrix theory.
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
Parareal algorithms are studied for semilinear parabolic stochastic partial differential equations. These algorithms proceed as two-level integrators, with fine and coarse schemes, and have been designed to achieve a `parallel in real time'…
We relate the $L_p$-variation, $2\le p < \infty$, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness…
Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach…