The concentration function problem for locally compact groups revisited
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Date
2011-02-17
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Non-dissipating space-time random walks, tau-decomposable laws and their continuous time analogues
Abstract
The concentration function problem for locally compact
groups, i.e., the structure of groups admitting adapted nondissipating
random walks, is closely related to relatively compact
M- or skew semigroups and corresponding space-time random walks,
resp. to tau-decomposable laws, where tau denotes an automorphism.
Analogous results are obtained in the case of continuous time:
Non-dissipating Lévy processes are related to relatively compact
distributions of generalized Ornstein Uhlenbeck processes and corresponding
space-time processes, resp. T-decomposable laws, T =(tau_t) denoting a continuous group of automorphisms acting on groups
of the form N = C_K(T).