Martingale-driven approximations of singular stochastic PDEs
arXiv:1808.09429
Abstract
We define multiple stochastic integrals with respect to càdlàg 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.
The article contains mistakes that have been corrected in arXiv:2303.10245