Stochastic equations and evolution families in the space of formal mappings

TL;DR

This paper studies stochastic equations for formal mappings, establishing conditions for existence, uniqueness, and the evolution of solutions within this mathematical framework.

Contribution

It introduces a rigorous analysis of stochastic equations in the space of formal mappings, proving fundamental properties like existence and uniqueness.

Findings

Proved existence of solutions for stochastic equations in formal mappings.

Established uniqueness of solutions under certain conditions.

Demonstrated the evolution property of solutions over time.

Abstract

We consider stochastic equations for the class of formal mappings. Existence and uniqueness of solution, as well as evolution property are proved.