Hazod, Wilfried2011-02-172011-02-172011-02-17http://hdl.handle.net/2003/2762710.17877/DE290R-14581The 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).en610preprint