### Abstract

Some finite and infinite dimensional perturbed alpha-stable dynamics are constructed
and studied in this paper. We prove that the finite dimensional system is strongly
mixing, while in the infinite dimensional case that the functional coercive inequal-
ities are not available, we develop and apply a technique to prove the point-wise
ergodicity for systems with suffciently small interaction in a large subspace of
omega= RZd .

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Eurandom |

Number of pages | 25 |

Publication status | Published - 2008 |

### Publication series

Name | Report Eurandom |
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Volume | 2008051 |

ISSN (Print) | 1389-2355 |

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## Cite this

Xu, L., & Zegarlinski, B. (2008).

*Ergodicity of the finite and infinite dimensional alpha-stable systems*. (Report Eurandom; Vol. 2008051). Eurandom.