Stochastic processes on non-Archimedean spaces. III. Stochastic processes on totally disconnected topological groups

Abstract

Stochastic processes on totally disconnected topological groups are investigated. In particular they are considered for diffeomorphism groups and loop groups of manifolds on non-Archimedean Banach spaces. Theorems about a quasi-invariance and a pseudo-differentiability of transition measures are proved. Transition measures are used for the construction of strongly continuous representations including irreducible of these groups. In addition stochastic processes on general Banach-Lie groups, loop monoids, loop spaces and path spaces of manifolds on Banach spaces over non-Archimedean local fields also are investigated.

36 pages, 0 figures, Latex

References in corpus (3)

• Stochastic processes on non-Archimedean spaces. II. Stochastic antiderivational equations
• Stochastic processes on non-Archimedean spaces. I. Stochastic processes on Banach spaces
• Stochastic processes on geometric loop and diffeomorphism groups of real and complex manifolds, associated unitary representations

Cited by in corpus (1)

• Algebras of non-Archimedean measures on groups