A discrete stochastic Gronwall Lemma

Abstract

We derive a discrete version of the stochastic Gronwall Lemma found in [Scheutzow, IDAQP, 2013]. 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 time discrete martingales. As an application the proof of an a priori estimate for the backward Euler-Maruyama method is included.