On large deviations of branching processes in a random environment: geometric distribution of descendants
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M. V. Kozlov
A branching process Zn with geometric distribution of descendants in a random environment represented by a sequence of independent identically distributed random variables (the Smith–Wilkinson model) is considered. The asymptotics of large deviation probabilities P(ln Zn > θn), θ > 0, are found provided that the steps of the accompanying random walk Sn satisfy the Cramér condition. In the cases of supercritical, critical, moderate, and intermediate subcritical processes the asymptotics follow that of the large deviations probabilities P(Sn ≤ θn). In strongly subcritical case the same asymptotics hold for θ greater than some θ* (for θ ≤ θ* the asymptotics of large deviation probabilities are different).
Copyright 2006, Walter de Gruyter
Articles in the same Issue
- Testing numbers of the form N = 2kpm − 1 for primality
- On a two-dimensional binary model of a financial market and its extension
- Stochastic optimality in the problem on linear regulator perturbed by a sequence of dependent random variables
- On large deviations of branching processes in a random environment: geometric distribution of descendants
- A random algorithm for multiselection
- On the mean complexity of monotone functions
- On reliability of circuits over the basis {x ∨ y ∨ z, x & y & z, } under single-type constant faults at inputs of elements
Articles in the same Issue
- Testing numbers of the form N = 2kpm − 1 for primality
- On a two-dimensional binary model of a financial market and its extension
- Stochastic optimality in the problem on linear regulator perturbed by a sequence of dependent random variables
- On large deviations of branching processes in a random environment: geometric distribution of descendants
- A random algorithm for multiselection
- On the mean complexity of monotone functions
- On reliability of circuits over the basis {x ∨ y ∨ z, x & y & z, } under single-type constant faults at inputs of elements
