A stochastic Schauder-Tychonoff type theorem and its applications
Probability
2026-02-23 v1 Analysis of PDEs
Functional Analysis
Abstract
One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our existence result to nonlinear stochastic diffusion equations with non-Lipschitz perturbations
Keywords
Cite
@article{arxiv.2602.17285,
title = {A stochastic Schauder-Tychonoff type theorem and its applications},
author = {Erika Hausenblas and Ankit Kumar and Jonas M. Tölle},
journal= {arXiv preprint arXiv:2602.17285},
year = {2026}
}