Electronic Journal of Probability
- Electron. J. Probab.
- Volume 25 (2020), paper no. 38, 55 pp.
A stochastic sewing lemma and applications
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 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.
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
Permanent link to this document
Digital Object Identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60H05: Stochastic integrals 60L20
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