Large deviation rates for Markov branching processes

Junping Li, Lan Cheng, Anthony G. Pakes, Anyue Chen, Liuyan Li

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Large deviation rates are determined for quantities associated with a Markov branching process (Xt:t ≥ 0) having offspring mean m (1,∞) and split rate a > 0. The principal quantities examined are P(|Xt+τ/Xt -exp(a(m - 1)t)| > ) and P(|W - Wt| > ), where W is the almost sure limit of an appropriately normed version of Xt. Modifications and conditional versions are examined. Some of this requires determination of the asymptotic behavior of harmonic moments E(Xt-r).

Original languageEnglish
Pages (from-to)447-468
Number of pages22
JournalAnalysis and Applications
Volume18
Issue number3
DOIs
Publication statusPublished - 1 Apr 2020

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