English

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}
}
R2 v1 2026-07-01T10:42:47.783Z