Long-time behaviour and regularity properties of transition semigroups of Fleming-Vioti processes

• 成果类型: Article
• 署名作者: Stannat, W
• 署名单位: University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400100166
• 发表日期: 2002
• 页码: 431-469
• 关键词: operators

摘要

Let A be a Feller generator on a compact space and L be the corresponding Fleming-Viot (FV) operator with no selection and no recombination. In this paper we give conditions on A implying that the semigroup (T-t) generated by L (i) converges towards equilibrium with exponential rate (moreover, we determine explicit bounds on the rate of convergence in terms of A), (ii) is hypercontractive, (iii) is strong Feller, and (iv) is compact, We give applications of the last result to the existence of invariant measures for FV-operators with interactive selection.