A discrete stochastic Gronwall lemma

作者：Kruse Raphael^*; Scheutzow Michael

来源：Mathematics and Computers in Simulation, 2018, 143: 149-157.

DOI：10.1016/j.matcom.2016.07.002

• Gronwall lemma
• Martingale inequality
• Backward Euler-Maruyama method
• A priori estimate

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.

• 出版日期2018-1