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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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