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Nonlinear branching processes with immigration

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Abstract

The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established.

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Acknowledgements

The author would like to thank Professors Mu-Fa Chen, Yong-Hua Mao and Yu-Hui Zhang for their advice and encouragement. I am grateful to the two referees for pointing out a number of typos in the first version of the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China

    Pei-Sen Li

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  1. Pei-Sen Li
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Correspondence to Pei-Sen Li.

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Supported by NSFC (Grant Nos. 1131003, 11626245 and 11571043)

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Li, PS. Nonlinear branching processes with immigration. Acta. Math. Sin.-English Ser. 33, 1021–1038 (2017). https://doi.org/10.1007/s10114-017-6472-0

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  • DOI: https://doi.org/10.1007/s10114-017-6472-0

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