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- W2950341024 abstract "Let $Z_{n,}n=0,1,...,$ be a branching process evolving in the random environment generated by a sequence of iid generating functions $% f_{0}(s),f_{1}(s),...,$ and let $S_{0}=0,S_{k}=X_{1}+...+X_{k},kgeq 1,$ be the associated random walk with $X_{i}=log f_{i-1}^{prime}(1),$ $tau (m,n)$ be the left-most point of minimum of $left{S_{k},kgeq 0right} $ on the interval $[m,n],$ and $T=min left{k:Z_{k}=0right} $. Assuming that the associated random walk satisfies the Doney condition $P(S_{n}>0) to rho in (0,1),nto infty ,$ we prove (under the quenched approach) conditional limit theorems, as $nto infty $, for the distribution of $Z_{nt},$ $Z_{tau (0,nt)},$ and $Z_{tau (nt,n)},$ $tin (0,1),$ given $T=n$. It is shown that the form of the limit distributions essentially depends on the location of $tau (0,n)$ with respect to the point $nt.$" @default.
- W2950341024 created "2019-06-27" @default.
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- W2950341024 date "2008-04-07" @default.
- W2950341024 modified "2023-09-27" @default.
- W2950341024 title "Branching processes in random environment die slowly" @default.
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