Occupation times of subcritical branching immigration systems with Markov motions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Milos, Piotr

关键词: Functional central limit theorem;    Occupation time fluctuations;    Branching particles systems with immigration;    Subcritical branching law;   

DOI  :  10.1016/j.spa.2009.04.003

来源: Elsevier

【 摘 要 】

We consider a branching system consisting of particles moving according to a Markov family in R-d and undergoing subcritical branching with a constant rate V > 0. New particles immigrate to the system according to it homogeneous space-time Poisson random field. The process of the fluctuations of the rescaled Occupation time is Studied with very mild assumptions on the Markov family. In this general setting a functional central limit theorem is proved. The subcriticality of the branching law is crucial for the limit behaviour and in a sense overwhelms the properties of the particles' motion. It is for this reason that the limit is the same for all dimensions and can be obtained for a wide class of Markov processes. Another consequence is the form of the limit-an S'(R-d)-valued Wiener process with a simple temporal structure and a complicated spatial one. This behaviour contrasts sharply with the case of critical branching systems. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free