Pathwise uniqueness for stochastic heat and damped equations with H\"older continuous drift
Probability
2025-09-22 v4
Abstract
In this paper, we prove pathwise uniqueness for stochastic differential equations in infinite dimension. Under our assumptions, we are able to consider the stochastic heat equation up to dimension , the stochastic damped wave equation in dimension and the stochastic Euler-Bernoulli damped beam equation up to dimension . We do not require that the so-called {\it structure condition} holds true.
Keywords
Cite
@article{arxiv.2308.05415,
title = {Pathwise uniqueness for stochastic heat and damped equations with H\"older continuous drift},
author = {Davide Addona and Davide A. Bignamini},
journal= {arXiv preprint arXiv:2308.05415},
year = {2025}
}
Comments
Added a section about weak existence, which combined with pathwise uniqueness, implies strong existence