A stochastic sewing lemma and applications

By Khoa Le. Electronic Journal of Probability, 2018

119 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ca7dd4798a14247c07a0c76e34d05e9407bf794a

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Citations in the corpus

Averaging dynamics driven by fractional Brownian motion (2019, methodology): “We resolve this problem by using a carefully chosen approximation to the Young integral and using a recently discovered stochastic sewing lemma by Lê [Lê18].”
Quantifying a convergence theorem of Gyöngy and Krylov (2021, methodology): “Instead of relying on PDE theory, it introduces an approach based on stochastic sewing [26].”
Noiseless regularisation by noise (2020, background): “This is in analogy with the results obtained in [35], Sections 6 and 7.”
Distribution dependent SDEs driven by additive fractional Brownian motion (2021, methodology): “Observe that ( q, p ) ∈ (1 , ∞ ) 2 satisfy (3.20) if and only if the conjugates ( q ′ , p ′ ) satisfy By [31, Lemma 6.4] (more precisely equation (6.11) right after the proof therein) and estimates based on Girsanov theorem analogous to the proof of Proposition 3.20, we deduce that x and so we can…”