Stochastic processes on non-Archimedean spaces. II. Stochastic antiderivational equations

TL;DR

This paper explores stochastic antiderivational equations on Banach spaces over non-Archimedean fields, establishing existence and uniqueness theorems, and examining Wiener processes in the context of non-Archimedean Gaussian measures.

Contribution

It introduces the theory of stochastic antiderivational equations in non-Archimedean spaces, providing foundational results on solutions and their properties.

Findings

Proved existence and uniqueness of solutions under specific conditions

Analyzed Wiener processes in relation to non-Archimedean Gaussian measures

Extended stochastic calculus to non-Archimedean Banach spaces

Abstract

Stochastic antiderivational equations on Banach spaces over local non-Archimedean fields are investigated. Theorems about existence and uniqiuness of the solutions are proved under definite conditions. In particular Wiener processes are considered in relation with the non-Archimedean analog of the Gaussian measure.