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Catalytic Discrete State Branching Models and Related Limit Theorems

Author

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  • Zenghu Li

    (Beijing Normal University)

  • Chunhua Ma

    (Nankai University)

Abstract

Catalytic discrete state branching processes with immigration are defined as strong solutions of stochastic integral equations. We provide main limit theorems of those processes using different scalings. The class of limit processes of the theorems includes essentially all continuous state catalytic branching processes and spectrally positive regular affine processes.

Suggested Citation

  • Zenghu Li & Chunhua Ma, 2008. "Catalytic Discrete State Branching Models and Related Limit Theorems," Journal of Theoretical Probability, Springer, vol. 21(4), pages 936-965, December.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:4:d:10.1007_s10959-008-0161-y
    DOI: 10.1007/s10959-008-0161-y
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Li, Zeng-Hu, 1992. "Measure-valued branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 249-264, December.
    6. Bingham, N. H., 1976. "Continuous branching processes and spectral positivity," Stochastic Processes and their Applications, Elsevier, vol. 4(3), pages 217-242, August.
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    Cited by:

    1. Foucart, Clément & Vidmar, Matija, 2024. "Continuous-state branching processes with collisions: First passage times and duality," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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