English

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 33, the stochastic damped wave equation in dimension 11 and the stochastic Euler-Bernoulli damped beam equation up to dimension 33. 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

R2 v1 2026-06-28T11:52:35.795Z