Large and Moderate Deviations for the Total Population Arising from a Sub-critical Galton–Watson Process with Immigration

Shihang Yu (), Dehui Wang and Xia Chen ()
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Shihang Yu: Qiqihar University
Dehui Wang: Jilin University
Xia Chen: University of Tennessee

Journal of Theoretical Probability, 2018, vol. 31, issue 1, 41-67

Abstract: Abstract In this paper, we provide the exact forms of large and moderate deviations for the empirical mean of population and the centered total population of a sub-critical branching process with immigration. The rate functions in our large and moderate deviations are explicitly identified. Our theorems also apply to the models of the integer-valued autoregression. In computing the generating function requested by Gärtner-Ellis theorem, our treatment substantially relies on an algorithm specifically designed for the autoregressive structure of our models.

Keywords: Branching process with immigration; Integer-valued AR model; Large deviations principle; Moderate deviation principle; 60J80; 60F10; 62M10; 62G20 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-016-0706-4

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