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 language | English |
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Pages (from-to) | 447-468 |
Number of pages | 22 |
Journal | Analysis and Applications |
Volume | 18 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Apr 2020 |