A stochastic sewing lemma and applications
Probability
2021-10-12 v5
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.
Cite
@article{arxiv.1810.10500,
title = {A stochastic sewing lemma and applications},
author = {Khoa Lê},
journal= {arXiv preprint arXiv:1810.10500},
year = {2021}
}
Comments
final version, to appear on EJP