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On large deviations of a branching process in random environments with immigration at moments of extinction
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Dmitriy V. Dmitruschenkov
Published/Copyright:
December 8, 2015
Abstract
Let (Z*n) be a branching process in independent identically distributed random environments with (conditioned on the environments) geometric distribution of the number of offsprings and immigration of independent identically distributed numbers of new particles at moments of extinction. Supposing that the increments of the accompanying random walk (Sn) and numbers of immigrants satisfy right-hand Cramér condition we obtain the asymptotics of large deviation probabilities P(ln Z*n ≥ θn).
Keywords : large deviations; Cramér condition; branching processes; random environments; processes with immigration
Received: 2014-8-6
Published Online: 2015-12-8
Published in Print: 2015-12-1
© 2015 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Cardinality estimates for some classes of regular languages
- On large deviations of a branching process in random environments with immigration at moments of extinction
- Existence of arbitrarily long square-free words with one possible mismatch
- On frequencies of elements in multicyclic random sequence modulo 4
- Single tests for logical gates
- On the probability of coincidence of cycle lengths for independent random permutations with given number of cycles
Keywords for this article
large deviations;
Cramér condition;
branching processes;
random environments;
processes with immigration
Articles in the same Issue
- Frontmatter
- Cardinality estimates for some classes of regular languages
- On large deviations of a branching process in random environments with immigration at moments of extinction
- Existence of arbitrarily long square-free words with one possible mismatch
- On frequencies of elements in multicyclic random sequence modulo 4
- Single tests for logical gates
- On the probability of coincidence of cycle lengths for independent random permutations with given number of cycles
