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Boundary Behaviors for a Continuous-state Nonlinear Neveu’s Branching Process

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Abstract

By generalizing a criterion of Mufa Chen for Markov jump processes, we establish the necessary and sufficient conditions for the extinction, explosion and coming down from infinity of a continuous-state nonlinear Neveu’s branching process.

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Acknowledgements

We are grateful to Pei-Sen Li, Zenghu Li and **aowen Zhou for their careful reading and insightful suggestions on the manuscript.

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Authors and Affiliations

  1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, P. R. China

    Lin Yu Bai & Xu Yang

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  1. Lin Yu Bai
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  2. Xu Yang
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Correspondence to Xu Yang.

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Conflict of Interest The authors declare no conflict of interest.

Additional information

Supported by NSFC (Grant No. 12061004), NSF of Ningxia (Grant No. 2021AAC02018), the Fundamental Research Funds for the Central Universities, North Minzu University (Grant No. 2020KYQD17), Major research project for North Minzu University (Grant No. ZDZX201902), and the Construction Project of First-Class Disciplines in Ningxia Higher Education (Grant No. NXYLXK2017B09)

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Bai, L.Y., Yang, X. Boundary Behaviors for a Continuous-state Nonlinear Neveu’s Branching Process. Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-2741-x

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  • DOI: https://doi.org/10.1007/s10114-024-2741-x

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