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April 8, 2026

Regularity of multiplicative processes on infinite-dimensional Lie groups

Puntos clave

The research aims to explore the regularity properties of multiplicative stochastic processes on infinite-dimensional Lie groups.
Studied conditions for cadlag (right-continuous with left limits) modifications of multiplicative processes.
Derived bounds on local behavior of these processes.
Utilized local equivalence between Banach-Lie groups and Banach spaces through exponential and logarithm functions.
Illustrated findings with multiplicative processes on the Heisenberg group.
Established conditions for the existence of cadlag modifications in stochastic processes on Lie groups.
Derivatives of local behavior bounded under specific analytic estimates.
Demonstrated structural results connecting Banach spaces and Lie groups through stochastic frameworks.

Resumen

This article studies regularity properties of multiplicative stochastic processes on infinite-dimensional Lie groups. We investigate conditions under which these processes admit cadlag 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. To illustrate our findings, we consider multiplicative processes on the Heisenberg group.

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