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Entrance Laws for Continuous-State Nonlinear Branching Processes Coming Down from Infinity

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2021-2022 MATRIX Annals

Part of the book series: MATRIX Book Series ((MXBS,volume 5))

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Abstract

We consider a class of non-negative valued, time-changed spectrally positive Lévy processes stopped whenever hitting 0, which can be identified as continuous-state branching processes with population dependent branching rates. Given the process comes down from infinity, we find expressions for Laplace transform of the first passage time and for the potential measure for the process started from infinity. Those expressions are in terms of the generalized scale functions for the corresponding spectrally positive Lévy processes.

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Author information

Authors and Affiliations

  1. School of Mathematics and LPMC, Nankai University, Tian**, China

    Bo Li

  2. Department of Mathematics and Statistics, Concordia University, Montreal, Canada

    **aowen Zhou

Authors
  1. Bo Li
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  2. **aowen Zhou
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Correspondence to **aowen Zhou .

Editor information

Editors and Affiliations

  1. School of Math, Rainforest Walk 9, Monash University, Melbourne, VIC, Australia

    David R. Wood

  2. School of Mathematics and Statistics, University of Melbourne, Melbourne, VIC, Australia

    Jan de Gier

  3. School of Mathematics and Statistics, University of Western Australia, Perth, WA, Australia

    Cheryl E. Praeger

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Li, B., Zhou, X. (2024). Entrance Laws for Continuous-State Nonlinear Branching Processes Coming Down from Infinity. In: Wood, D.R., de Gier, J., Praeger, C.E. (eds) 2021-2022 MATRIX Annals. MATRIX Book Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-031-47417-0_25

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