A chaotic representation property of the multidimensional Dunkl processes

• 成果类型: Article
• 署名作者: Gallardo, Leonard; Yor, Marc
• 署名单位: Universite de Tours; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000133
• 发表日期: 2006
• 页码: 1530-1549
• 关键词: markov-processes; Operators; equation

摘要

Dunkl processes are martingales as well as cadlag homogeneous Markov processes taking values in R-d and they are naturally associated with a root system. In this paper we study the jumps of these processes, we describe precisely their martingale decompositions into continuous and purely discontinuous parts and we obtain a Wiener chaos decomposition of the corresponding L-2 spaces of these processes in terms of adequate mixed multiple stochastic integrals.