Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions
Analysis of PDEs
2019-09-27 v5 Functional Analysis
Probability
Abstract
We prove existence and uniqueness of solutions to a nonlinear stochastic evolution equation on the -dimensional torus with singular -Laplace-type or total variation flow-type drift with general sublinear doubling nonlinearities and Gaussian gradient Stratonovich noise with divergence-free coefficients. Assuming a weak defective commutator bound and a curvature-dimension condition, the well-posedness result is obtained in a stochastic variational inequality setup by using resolvent and Dirichlet form methods and an approximative It\^{o}-formula.
Keywords
Cite
@article{arxiv.1803.07005,
title = {Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions},
author = {Jonas M. Tölle},
journal= {arXiv preprint arXiv:1803.07005},
year = {2019}
}
Comments
26 pages, 58 references. Essential changes to Version 4: Examples revised. Accepted for publication in Stochastic Processes and their Applications