Electronic Journal of Probability

A stochastic sewing lemma and applications

Khoa Lê

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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

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

Received: 27 October 2018
Accepted: 6 March 2020
First available in Project Euclid: 31 March 2020

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Digital Object Identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60H05: Stochastic integrals 60L20

sewing lemma Doob-Meyer decomposition rough paths regularization by noise stochastic differential equations fractional Brownian motion additive functional chaos expansion

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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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