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Occupation times for age-structured branching processes

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  • Cheng, Ziling

Abstract

We consider occupation time processes for the age-structured branching processes with or without immigration introduced by Ji and Li (2022). Two large number laws and a central limit theorem for occupation times of the model with immigration are obtained.

Suggested Citation

  • Cheng, Ziling, 2024. "Occupation times for age-structured branching processes," Statistics & Probability Letters, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:stapro:v:211:y:2024:i:c:s0167715224001147
    DOI: 10.1016/j.spl.2024.110145
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    References listed on IDEAS

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    1. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems I: Long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 1-18, January.
    2. Donald A. Dawson & Klaus Fleischmann, 1997. "A Continuous Super-Brownian Motion in a Super-Brownian Medium," Journal of Theoretical Probability, Springer, vol. 10(1), pages 213-276, January.
    3. Hong, Wenming, 2002. "Longtime behavior for the occupation time process of a super-Brownian motion with random immigration," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 43-62, November.
    4. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    5. I. Kaj & S. Sagitov, 1998. "Limit Processes for Age-Dependent Branching Particle Systems," Journal of Theoretical Probability, Springer, vol. 11(1), pages 225-257, January.
    6. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    7. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems II: Critical and large dimensions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 19-35, January.
    8. D. A. Dawson & L. G. Gorostiza & A. Wakolbinger, 2001. "Occupation Time Fluctuations in Branching Systems," Journal of Theoretical Probability, Springer, vol. 14(3), pages 729-796, July.
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