The Heckman-Opdam Markov processes

• 成果类型: Article
• 署名作者: Schapira, Bruno
• 署名单位: Universite de Orleans; Universite Paris Cite; Sorbonne Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0034-1
• 发表日期: 2007
• 页码: 495-519
• 关键词: dunkl operators; Brownian bridge; ALGEBRAS; motion

摘要

We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale decomposition of the radial part, and some properties of the jumps. We prove also a law of large numbers, a central limit theorem, and the convergence of the normalized process to the Dunkl process. Eventually we describe the asymptotic behavior of the infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric spaces setting in (Iberoamericana 18:41-97, 2002).