A discrete stochastic Gronwall Lemma

Raphael Kruse; Michael Scheutzow

doi:10.1016/j.matcom.2016.07.002

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arXiv · 1601.07503

A discrete stochastic Gronwall Lemma

Raphael Kruse·Michael Scheutzow

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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.

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Raphael Kruse, Michael Scheutzow. 2016-01-27. A discrete stochastic Gronwall Lemma. https://doi.org/10.1016/j.matcom.2016.07.002

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