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.
Publié le : 2006-05-14
Classification:
Skew convolution semigroup,
affine process,
continuous state branching process,
catalytic branching process,
immigration,
Ornstein–Uhlenbeck process,
stochastic integral equation,
Poisson random measure,
60J35,
60J80,
60H20,
60K37
@article{1151418494,
author = {Dawson, D. A. and Li, Zenghu},
title = {Skew convolution semigroups and affine Markov processes},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 1103-1142},
language = {en},
url = {http://dml.mathdoc.fr/item/1151418494}
}
Dawson, D. A.; Li, Zenghu. Skew convolution semigroups and affine Markov processes. Ann. Probab., Tome 34 (2006) no. 1, pp. 1103-1142. http://gdmltest.u-ga.fr/item/1151418494/