Quasi-invariance and Gibbs structure of diffusion measures on infinite product groups - Daletskii, A.; Albeverio, S. (Methods of Functional Analysis and Topology, 2025)
We prove a quasi-invariance property for the distribution of solutions to a stochastic differential equation on an infinite dimensional Lie group G constructed as the countable power of a compact Lie group G. In the gradient case, we prove the Gibbs structure of the distribution and construct the associated ’’diffusion bridge’’ measure on the loop space of G.