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A Multilevel birth-death particle system and its continuous diffusion

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  01 July 2016

Yadong Wu
Yadong Wu*
Affiliation:
Carleton University
*
∗ Postal address: Department of Mathematics and Statistics, Carleton University, Ottawa, Canada K15 5B6.
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Abstract

In this paper we introduce a multilevel birth-death particle system and consider its diffusion approximation which can be characterized as a M([R+)-valued process. The tightness of rescaled processes is proved and we show that the limiting M(R+)-valued process is the unique solution of the M([R+)-valued martingale problem for the limiting generator. We also study the moment structures of the limiting diffusion process.

Keywords

MULTILEVEL BIRTH-DEATH PROCESSTIGHTNESSMARTINGALE PROBLEMDIFFUSION APPROXIMATIONMEASURE-VALUED PROCESSMOMENT STRUCTURE

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J60: Diffusion processes 60J57: Multiplicative functionals 60F05: Central limit and other weak theorems
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 3 , September 1993 , pp. 549 - 569
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Supported partially by a scholarship from the Faculty of Graduate Studies and Research of Carleton University, Ottawa, and by a NSERC Canada grant to D. Dawson.

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