Skew convolution semigroups and affine Markov processes
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 nonLipschitz coefficients and Poissontype 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505444
 arXiv:
 arXiv:math/0505444
 Bibcode:
 2005math......5444D
 Keywords:

 Mathematics  Probability;
 Mathematics  Statistics;
 60J35 (Primary) 60J80;
 60H20;
 60K37 (Secondary)
 EPrint:
 Published at http://dx.doi.org/10.1214/009117905000000747 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)