Skew convolution semigroups and affine Markov processes

• 成果类型: Article
• 署名作者: Dawson, D. A.; Li, Zenghu
• 署名单位: Carleton University; Beijing Normal University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000747
• 发表日期: 2006
• 页码: 1103-1142
• 关键词: generalized mehler semigroups; branching-processes

摘要

A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficients and Poisson-type integrals over some random sets. Based on this characterization, it is proved that the affine process arises naturally in a limit theorem for the difference of a pair of reactant processes in a catalytic branching system with immigration.