Regularity of multiplicative processes on infinite-dimensional Lie groups

Key Points

• 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.