A discrete stochastic Gronwall Lemma
arXiv:1601.0750317 citationsh-index: 36
Originality Synthesis-oriented
AI Analysis
Provides a theoretical tool for analyzing numerical methods for stochastic differential equations, but the result is incremental.
The authors derive a discrete version of the stochastic Gronwall lemma and use it to prove an a priori estimate for the backward Euler-Maruyama method.
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.