Rate of Convergence of Space Time Approximations for stochastic evolution equations

TL;DR

This paper analyzes the convergence rates of numerical approximations for stochastic evolution equations in Banach spaces, providing estimates under specific regularity, monotonicity, and Lipschitz conditions, with applications to parabolic stochastic PDEs.

Contribution

It introduces a general framework for estimating convergence rates of space-time approximations for stochastic evolution equations with unbounded operators, extending to quasilinear stochastic PDEs.

Findings

Convergence rates are established under strong monotonicity and Lipschitz conditions.

The framework applies to a broad class of quasilinear stochastic PDEs.

Explicit estimates depend on regularity and consistency conditions.

Abstract

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type.