A stochastic sewing lemma and applications. (English) Zbl 1480.60162

In this paper, the author introduced a stochastic version of Gubinelli’s sewing lemma and established a sufficient condition for the convergence in moments of some random Riemann sums. Based on this, the regularity restriction is improved by a half. Moreover, the author showed a Doob-Meyertype decomposition through the limiting process and provided relations with Itô calculus. Finally, the author investigated stochastic differential equations driven by Brownian motions or fractional Brownian motions with irregular drifts using the stochastic sewing lemma.


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
60L20 Rough paths
Full Text: DOI arXiv Euclid


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