Abstract
Under various conditions, sewing lemmas provide convergence of the Riemann-type sum $\sum_{[s,t]} \varXi_{s,t}$ for a given two-parametric map $\varXi$ as the mesh size of the considered partitions tends to zero. This talk will present a stochastic sewing lemma for two-parameter processes whose increments, when viewed as functions with values in $L^m(\Omega;\mathbb{V})$ for $m\geq 2$ and a real separable Banach space $\mathbb{V}$ with a non-trivial martingale type, are of Besov regularity.
The contribution is two-fold: First, the stochastic sewing lemma of L\^e [Electron.\ J.\ Probab.\ 25(38): 1--55 (2020)] is generalized for processes whose increments belong to a Besov and not necessarily H\"older space. Second, the assumptions of the Besov sewing lemma of Friz et al. [J.\ Differ.\ Equ.\ 339(4): 152--231 (2022)] can be relaxed if stochastics is incorporated in the sewing from the beginning.