Lê, K orcid.org/0000-0002-7654-7139 (2020) A stochastic sewing lemma and applications. Electronic Journal of Probability, 25 (38). pp. 1-55. ISSN 1083-6489
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.
Metadata
Item Type: | Article |
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Authors/Creators: | |
Copyright, Publisher and Additional Information: | © 2023 Project Euclid. This is an open access article published under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | sewing lemma; Doob-Meyer decomposition; rough paths; regularization by noise; stochastic differential equations; fractional Brownian motion; additive functional; chaos expansion |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 May 2023 15:46 |
Last Modified: | 26 May 2023 15:46 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Identification Number: | 10.1214/20-EJP442 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198430 |
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