FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1091-1105

Stochastic processes on groups of diffeomorphisms and loops of real, complex and non-Archimedean manifolds

S. V. Ludkovsky

Abstract

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The article is devoted to stochastic processes on infinite dimensional topological groups that do not satisfy the Campbell--Hausdorff formula even locally. In the cases of real and complex manifolds the classical stochastic analysis is used, but in the non-Archimedean case the corresponding stochastic antiderivations and antiderivational equations are developed and investigated. For real-valued transition probabilities of random processes the corresponding regular strongly continuous unitary representations are constructed and their topological irreducibility is analysed.

All articles are published in Russian.

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Last modified: April 17, 2002