The Annals of Probability

Skew convolution semigroups and affine Markov processes

D. A. Dawson and Zenghu Li

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Abstract

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.

Article information

Source
Ann. Probab., Volume 34, Number 3 (2006), 1103-1142.

Dates
First available in Project Euclid: 27 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1151418494

Digital Object Identifier
doi:10.1214/009117905000000747

Mathematical Reviews number (MathSciNet)
MR2243880

Zentralblatt MATH identifier
1102.60065

Subjects
Primary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60H20: Stochastic integral equations 60K37: Processes in random environments

Keywords
Skew convolution semigroup affine process continuous state branching process catalytic branching process immigration Ornstein–Uhlenbeck process stochastic integral equation Poisson random measure

Citation

Dawson, D. A.; Li, Zenghu. Skew convolution semigroups and affine Markov processes. Ann. Probab. 34 (2006), no. 3, 1103--1142. doi:10.1214/009117905000000747. https://projecteuclid.org/euclid.aop/1151418494


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