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

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.