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Lê, Khoa

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

Electron. J. Probab. 25, Paper No. 38, 55 p. (2020).
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.
Reviewer: Chao Wang (Kunming)

Cited in 1 Review
Cited in 18 Documents

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
60L20 Rough paths

Keywords:

sewing lemma; Doob-Meyer decomposition; rough paths; regularization by noise; stochastic differential equations; fractional Brownian motion; additive functional; chaos expansion.
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\textit{K. Lê}, Electron. J. Probab. 25, Paper No. 38, 55 p. (2020; Zbl 1480.60162)
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