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arXiv · 1810.10500

A stochastic sewing lemma and applications

Khoa Lê
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Abstract

We introduce a stochastic version of Gubinelli's sewing lemma, providing a sufficient condition for the convergence in moments of some random Riemann sums. Compared with the deterministic sewing lemma, adaptiveness is required and the regularity restriction is improved by a half. The limiting process exhibits a Doob-Meyer-type decomposition. Relations with It\^o calculus are established. To illustrate further potential applications, we use the stochastic sewing lemma in studying stochastic differential equations driven by Brownian motions or fractional Brownian motions with irregulardrifts.

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Khoa Lê. 2018-10-24. A stochastic sewing lemma and applications. https://doi.org/10.1214/20-ejp442

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