Regularity of multiplicative processes on infinite-dimensional Lie groups

TL;DR

This paper investigates the regularity of multiplicative stochastic processes on infinite-dimensional Lie groups, focusing on conditions for cadlag modifications and bounds on local behavior using Banach-Lie group techniques.

Contribution

It introduces a method to analyze regularity of stochastic processes on infinite-dimensional Lie groups by leveraging the exponential and logarithm mappings.

Findings

Conditions for cadlag modifications of processes

Bounds on local behavior of processes

Transfer of estimates via exponential and logarithm maps

Abstract

This article studies regularity properties of multiplicative stochastic processes on infinite-dimensional Lie groups. We investigate conditions under which these processes admit c\`adl\`ag modifications and derive bounds on their local behavior. Our approach builds on the local equivalence of Banach-Lie groups and Banach spaces via the exponential and logarithm, allowing us to transfer analytic estimates and structural results.