 Occupation times of subcritical branching immigration systems with Markov motionsPiotr Milos Stochastic Processes and their Applications, 2009, vol. 119, issue 10, 3211-3237 Abstract: We consider a branching system consisting of particles moving according to a Markov family in and undergoing subcritical branching with a constant rate V>0. New particles immigrate to the system according to a 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 -valued Wiener process with a simple temporal structure and a complicated spatial one. This behaviour contrasts sharply with the case of critical branching systems. Keywords: Functional; central; limit; theorem; Occupation; time; fluctuations; Branching; particles; systems; with; immigration; Subcritical; branching; law (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:119:y:2009:i:10:p:3211-3237 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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