A Stochastic Difference Equation with Stationary Noise on Groups
| Autor: | C. R. E. Raja |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
60B15
60G50 Pure mathematics Group (mathematics) Differential equation General Mathematics Probability (math.PR) 010102 general mathematics Torus Dynamical Systems (math.DS) Locally compact group Automorphism 01 natural sciences 0103 physical sciences FOS: Mathematics ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Coset 010307 mathematical physics Mathematics - Dynamical Systems 0101 mathematics Random variable Mathematics - Probability Mathematics Probability measure |
| Zdroj: | Canadian Journal of Mathematics. 64:1075-1089 |
| ISSN: | 1496-4279 0008-414X |
| DOI: | 10.4153/cjm-2011-094-6 |
| Popis: | We consider the stochastic difference equation on a locally compact group G, where is an automorphism of G, ξk are given G-valued random variables and ηk are unknown G-valued random variables. This equation was considered by Tsirelson and Yor on a one-dimensional torus. We consider the case when ξk have a common law μ and prove that if G is a distal group and is a distal automorphism of G and if the equation has a solution, then extremal solutions of the equation are in one-to-one correspondence with points on the coset space K\G for some compact subgroup K of G such that μ is supported on for any z in the support of μ. We also provide a necessary and sufficient condition for the existence of solutions to the equation. |
| Databáze: | OpenAIRE |
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