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May 2006 Skew convolution semigroups and affine Markov processes
D. A. Dawson, Zenghu Li
Ann. Probab. 34(3): 1103-1142 (May 2006). DOI: 10.1214/009117905000000747


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.


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D. A. Dawson. Zenghu Li. "Skew convolution semigroups and affine Markov processes." Ann. Probab. 34 (3) 1103 - 1142, May 2006.


Published: May 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1102.60065
MathSciNet: MR2243880
Digital Object Identifier: 10.1214/009117905000000747

Primary: 60J35
Secondary: 60H20 , 60J80 , 60K37

Keywords: Affine process , catalytic branching process , continuous state branching process , immigration , Ornstein–Uhlenbeck process , Poisson random measure , Skew convolution semigroup , Stochastic integral equation

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 3 • May 2006
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