Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3

Numerische Analyse äquivarianter Evolutionsgleichungen

10-005 Raphael Kruse.
Two-sided error estimates for stochastic onestep and multistep methods

This paper presents a unifying theory for the numerical analysis of stochastic onestep and multistep methods. In addition to well-known results on the error of strong convergence we prove a two-sided error estimate. This is characterized by Dahlquist's strong root condition and is used to determine the maximum order of convergence. In particular, we apply our theory to the stochastic theta method, BDF2-Maruyama and higher order Itô-Taylor schemes. The main ingredient of the stability analysis is a stochastic version of Spijker' norm.