Abstract
The purpose of this paper is the derivation of a discrete version of the stochastic Gronwall lemma involving a martingale. The proof is based on a corresponding deterministic version of the discrete Gronwall lemma and an inequality bounding the supremum in terms of the infimum for discrete time martingales. As an application the proof of an a priori estimate for the backward Euler-Maruyama method is included.
Type
Publication
Mathematics and Computers in Simulation, vol. 143, 149-157
Raphael Kruse
Professor
Prof. Dr. Raphael Kruse is the head of the working group “Numerik stochastischer Differentialgleichungen” at Martin-Luther-University Halle-Wittenberg. His research interests include numerical methods and stochastic analysis for stochastic evolution equations and Monte Carlo methods.