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Moments and large deviations for supercritical branching processes with immigration in random environments

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Abstract

Let (Zn) be a branching process with immigration in a random environment ξ, where ξ is an independent and identically distributed sequence of random variables. We show asymptotic properties for all the moments of Zn and describe the decay rates of the n-step transition probabilities. As applications, a large deviation principle for the sequence log Zn is established, and related large deviations are also studied.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, China

    Chunmao Huang

  2. School of Data and Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Chen Wang

  3. School of Mathematics and Statistics, Shandong University, Weihai, 264209, China

    Xiaoqiang Wang

Authors
  1. Chunmao Huang
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  2. Chen Wang
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  3. Xiaoqiang Wang
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Corresponding author

Correspondence to Xiaoqiang Wang.

Additional information

This work was partially supported by the National Nature Science Foundation of China (11601286, 11501146).

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Huang, C., Wang, C. & Wang, X. Moments and large deviations for supercritical branching processes with immigration in random environments. Acta Math Sci 42, 49–72 (2022). https://doi.org/10.1007/s10473-022-0102-3

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  • DOI: https://doi.org/10.1007/s10473-022-0102-3

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