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On large deviations of branching processes in a random environment with arbitrary initial number of particles: critical and supercritical cases
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A. V. Shklyaev
Published/Copyright:
June 22, 2013
Abstract
Given a sequence of independent identically distributed random variables i , we consider the branching process Zn in a random environment . It is known that under some suitable assumptions the probabilities of large deviations (greater than n) of lnZn and that of its associated random walk Sn are connected by the relation
P(lnZn ≥ θn |Z0= 1) ~ I(θ)P(Sn ≥ θn), n → ∞,
where I(θ) > 0. We obtain similar result for P(lnZn ≥ θn + ln m|Z0 = m) for n→ ∞ and m being finite or tending to infinity.
Published Online: 2013-06-22
Published in Print: 2012-10
© 2013 by Walter de Gruyter GmbH & Co.
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- On solutions and algebraic duality of generalised linear discrete time systems
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