## Electronic Journal of Probability

### A stochastic sewing lemma and applications

Khoa Lê

#### Abstract

We introduce a stochastic version of Gubinelli’s sewing lemma ([18]), 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 Itô 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 irregular drifts.

#### Article information

Source
Electron. J. Probab., Volume 25 (2020), paper no. 38, 55 pp.

Dates
Accepted: 6 March 2020
First available in Project Euclid: 31 March 2020

https://projecteuclid.org/euclid.ejp/1585620093

Digital Object Identifier
doi:10.1214/20-EJP442

Subjects
Secondary: 60H05: Stochastic integrals 60L20

#### Citation

Lê, Khoa. A stochastic sewing lemma and applications. Electron. J. Probab. 25 (2020), paper no. 38, 55 pp. doi:10.1214/20-EJP442. https://projecteuclid.org/euclid.ejp/1585620093

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