Stochastic sewing with Besov regularity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10502217" target="_blank" >RIV/00216208:11320/25:10502217 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=hsZ5.0Vzg9" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=hsZ5.0Vzg9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1051/ps/2025013" target="_blank" >10.1051/ps/2025013</a>

Result language
angličtina
Original language name
Stochastic sewing with Besov regularity
Original language description
Under various conditions, sewing lemmas provide convergence of the Riemann-type sum $sum_{[s,t]inpi} varXi_{s,t}$ for a given two-parametric map $varXi$ as the mesh sizes of the considered partitions $pi$ tend to zero. In this note, we prove a stochastic sewing lemma for two-parameter processes whose increments, when viewed as functions with values in $L^m(Omega;V)$ for $mgeq 2$ and a real separable Banach space $V$ with a non-trivial martingale type, are of Besov regularity. The contribution is two-fold: First, we generalize the stochastic sewing lemma of L^e [Electron. J. Probab. 25(38): 1--55 (2020)] for processes whose increments belong to a Besov and not necessarily H"older space. Second, we show here that 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. As an application, Besov regularity of the It^o integral of Brownian functionals is obtained.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GA22-12790S" target="_blank" >GA22-12790S: Stochastic systems in infinite dimensions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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