Asymptotics of parameterized exponential integrals given by Brownian motion on globally subanalytic sets

TL;DR

This paper studies the asymptotic behavior of parameterized exponential integrals related to Brownian motion on globally subanalytic sets, providing results on their definability and asymptotic expansions.

Contribution

It introduces new definability results and asymptotic expansions for exponential integrals associated with Brownian motion on globally subanalytic sets.

Findings

Establishes definability of the integrals

Derives asymptotic expansions for the integrals

Provides a framework for analyzing Brownian motion on complex sets

Abstract

We consider parameterized exponential integrals coming from the time evolution of the probability distribution of Brownian motion on globally subanalytic sets. We establish definability results and asymptotic expansions.