Martingale-driven approximations of singular stochastic PDEs
Probability
2023-03-27 v2 Analysis of PDEs
Abstract
We define multiple stochastic integrals with respect to c\`{a}dl\`{a}g martingales and prove moment bounds and chaos expansions, which allow to work with them in a way similar to Wiener stochastic integrals. In combination with the discretization framework of Erhard and Hairer (2017), our results give a tool for proving convergence of interacting particle systems to stochastic PDEs using regularity structures. As examples, we prove convergence of martingale-driven discretizations of the -dimensional stochastic quantization equation and the KPZ equation.
Cite
@article{arxiv.1808.09429,
title = {Martingale-driven approximations of singular stochastic PDEs},
author = {Konstantin Matetski},
journal= {arXiv preprint arXiv:1808.09429},
year = {2023}
}
Comments
The article contains mistakes that have been corrected in arXiv:2303.10245