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A stochastic sewing lemma and applications (1810.10500v5)
Published 24 Oct 2018 in math.PR
Abstract: 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 It^o 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 irregulardrifts.