An integrable bound for semilinear rough partial differential equations with unbounded diffusion coefficients
Probability
2025-03-07 v1
Abstract
This work develops moment bounds for the controlled rough path norm of the solution of semilinear rough partial differential equations.~The novel aspects are two-fold: first we consider rough paths of low time regularity and second treat unbounded diffusion coefficients. To this aim we introduce a suitable notion of a controlled rough path according to a monotone scale of Banach spaces and innovative control functions.
Cite
@article{arxiv.2503.04415,
title = {An integrable bound for semilinear rough partial differential equations with unbounded diffusion coefficients},
author = {Alexandra Blessing and Mazyar Ghani Varzaneh},
journal= {arXiv preprint arXiv:2503.04415},
year = {2025}
}