The concentration function problem for locally compact groups revisited: nondissipating space-time random walks, \(\tau\)-decomposable laws, and their continuous time analogues (Q2337046)

Summary: The concentration function problem for locally compact groups is concerned with the structure of groups admitting adapted nondissipating random walks. It is closely related to discrete relatively compact M- or skew convolution semigroups and corresponding space-time random walks, and to \(\tau\)-decomposable laws, respectively, where \(\tau\) denotes an automorphism. Analogous results are obtained in the case of continuous time: nondissipating Lévy processes are related to relatively compact distributions of generalized Ornstein-Uhlenbeck processes and corresponding space-time processes and to \(T\)-decomposable laws, respectively with \(T =(\tau_t)\) denoting a continuous group of automorphisms acting as contracting mod. a compact subgroup.