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

Arcady Ponosov

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arXiv · 2208.00674

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

Arcady Ponosov

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Abstract

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.

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Arcady Ponosov. 2022-08-01. A fixed-point theorem for local operators with applications to stochastic equations. https://arxiv.org/abs/2208.00674

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