scholarly journals Polynomial Growth, Recurrence and Ergodicity for Random Walks on Locally Compact Groups and Homogeneous Spaces

2011 ◽  
pp. 65-74
Author(s):  
Yves Guivarc’h ◽  
C. R. E. Raja
Keyword(s):  
Random Walks ◽  
Polynomial Growth ◽  
Homogeneous Spaces ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

Ergodic and mixing random walks on locally compact groups

1981 ◽  
Vol 257 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Joseph Rosenblatt
Keyword(s):  
Random Walks ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

scholarly journals The Concentration Function Problem for Locally Compact Groups Revisited: Nondissipating Space-Time Random Walks, -Decomposable Laws, and Their Continuous Time Analogues

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Wilfried Hazod
Keyword(s):  
Random Walks ◽  
Continuous Time ◽  
Compact Subgroup ◽  
Concentration Function ◽  
Space Time ◽  
Locally Compact Groups ◽  
Continuous Group ◽  
Compact Groups ◽  
Locally Compact ◽  
Convolution Semigroups

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 -decomposable laws, respectively, where 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 -decomposable laws, respectively with denoting a continuous group of automorphisms acting as contracting mod. a compact subgroup.

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