Preprint of the project:
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.
