A fixed-point theorem for local operators with applications to stochastic equations

Arcady Ponosov

Published 2022-08-01Version 1

We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative examples explain how this analysis can be applied to stochastic differential equations.