TY - JOUR A2 - Meyer, Ralf AU - Hazod, Wilfried PY - 2013 DA - 2013/10/23 TI - The Concentration Function Problem for Locally Compact Groups Revisited: Nondissipating Space-Time Random Walks, -Decomposable Laws, and Their Continuous Time Analogues SP - 540471 VL - 2013 AB - 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 τ-decomposable laws, respectively, where τ 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=τt denoting a continuous group of automorphisms acting as contracting mod. a compact subgroup. SN - 2314-4629 UR - https://doi.org/10.1155/2013/540471 DO - 10.1155/2013/540471 JF - Journal of Mathematics PB - Hindawi Publishing Corporation KW - ER -