MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS

doi:10.1007/s10473-022-0102-3

Abstract

Abstract: Let (Z_n) 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 Z_n and describe the decay rates of the n-step transition probabilities. As applications, a large deviation principle for the sequence log Z_n is established, and related large deviations are also studied.

Key words: branching process with immigration, random environment, moments, harmonic moments, large deviations

CLC Number:

60J80

Chunmao HUANG, Chen WANG, Xiaoqiang WANG. MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS[J].Acta mathematica scientia,Series B, 2022, 42(1): 49-72.

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