Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-06-08T06:25:08.089Z Has data issue: false hasContentIssue false
  • English
  • Français

An extended class of time-continuous branching processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Rong-Rong Chen
Rong-Rong Chen*
Affiliation:
University of Illinois at Urbana-Champaign
*
∗Postal address: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is devoted to studying an extended class of time-continuous branching processes, motivated by the study of stochastic control theory and interacting particle systems. The uniqueness, extinction, recurrence and positive recurrence criteria for the processes are presented. The main new point in our proofs is the use of several different comparison methods. The resulting picture shows that the methods are effective and hence should also be meaningful in other situations.

Keywords

BRANCHING PROCESSESUNIQUENESSRECURRENCEPOSITIVE RECURRENCE

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 14 - 23
Copyright
Copyright © Applied Probability Trust 1997 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Anderson, W. J. (1991) Continuous-Time Markov Chains. Springer, Berlin.Google Scholar
[2] Asmussen, S. and Hering, H. (1983) Branching Processes. Birkhäuser, Basel.Google Scholar
[3] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer, Berlin.Google Scholar
[4] Chen, M. F. (1991) On three classical problems for Markov chains with continuous time parameters. J. Appl. Prob. 28, 305–320.Google Scholar
[5] Chen, M. F. (1992) From Markov Chains to Non-Equilibrium Particle Systems. World Scientific, Singapore.Google Scholar
[6] Gao, S. Z. (1992) Linear controlled branching processes. (In Chinese.) Wuhan J. Math. 92, 415–122.Google Scholar
[7] Harris, T. E. (1963) Branching Processes. Springer, Berlin.Google Scholar
[8] Hou, Z. T. and Guo, Q. F. (1978) Time-Homogeneous Markov Processes with Countable State Space. (In Chinese.) Beijing Science Press, Beijing.Google Scholar
[9] Pakes, A. G. and Tavaré, S. (1981) Comments on the age distribution of Markov processes. Adv. Appl. Prob. 13, 681–703.Google Scholar
[10] Yamazato, M. (1975) Some results on continuous time branching process with state-dependent immigration. J. Math. Soc. Japan 17, 479–497.Google Scholar
[11] Yan, S. J. and Chen, M. F. (1986) Multidimensional Q-processes. Chin. Ann. Math. 7, 90–110.Google Scholar