International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 48, Pages 3067-3089
doi:10.1155/S0161171203108162
Stochastic processes on totally disconnected topological groups
Theoretical Department, Institute of General Physics, Russian Academy of Sciences, 38 Vavilov Street, Moscow 119991, GSP-1, Russia
Received 27 August 2001
Copyright © 2003 S. V. Ludkovsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 pseudodifferentiability of transition measures are proved.
Transition measures are used for the construction of strongly
continuous representations including the irreducible ones 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 are
also investigated.