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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 48, Pages 3067-3089

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 Hindawi Publishing Corporation. 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.


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.