Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient
Probability
2018-06-08 v2 Analysis of PDEs
Abstract
We provide new regularity results for the solutions of the Kolmogorov equation associated to a SPDE with nonlinear diffusion coefficients and a Burgers type nonlinearity. This generalizes previous results in the simpler cases of additive or affine noise. The basic tool is a discrete version of a two sided stochastic integral which allows a new formulation for the derivatives of these solutions. We show that this can be used to generalize the weak order analysis performed in [16]. The tools we develop are very general and can be used to study many other examples of applications.
Cite
@article{arxiv.1703.01095,
title = {Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient},
author = {Charles-Edouard Bréhier and Arnaud Debussche},
journal= {arXiv preprint arXiv:1703.01095},
year = {2018}
}