Open Access
2020 A stochastic sewing lemma and applications
Khoa Lê
Electron. J. Probab. 25: 1-55 (2020). DOI: 10.1214/20-EJP442


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.


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Khoa Lê. "A stochastic sewing lemma and applications." Electron. J. Probab. 25 1 - 55, 2020.


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

zbMATH: 07206375
MathSciNet: MR4089788
Digital Object Identifier: 10.1214/20-EJP442

Primary: 60H10
Secondary: 60H05 , 60L20

Keywords: additive functional , chaos expansion , Doob-Meyer decomposition , fractional Brownian motion , Regularization by noise , Rough paths , sewing lemma , Stochastic differential equations

Vol.25 • 2020
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