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- W2963392012 abstract "Consider a heavy-tailed branching process (denoted by $Z_{n}$) in random environments, under the condition which infers that $mathbb{E} log m(xi _{0})=infty $. We show that (1) there exists no proper $c_{n}$ such that ${Z_{n}/c_{n}}$ has a proper, non-degenerate limit; (2) normalized by a sequence of functions, a proper limit can be obtained, i.e., $y_{n}left (bar{xi } ,Z_{n}(bar{xi } )right )$ converges almost surely to a random variable $Y(bar{xi } )$, where $Yin (0,1)~eta $-a.s.; (3) finally, we give the necessary and sufficient conditions for the almost sure convergence of $left {frac{U(bar {xi },Z_{n}(bar {xi }))} {c_{n}(bar{xi } )}right }$, where $U(bar{xi } )$ is a slowly varying function that may depend on $bar{xi } $." @default.
- W2963392012 created "2019-07-30" @default.
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- W2963392012 date "2019-01-01" @default.
- W2963392012 modified "2023-09-25" @default.
- W2963392012 title "Asymptotic behaviour of heavy-tailed branching processes in random environments" @default.
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- W2963392012 doi "https://doi.org/10.1214/19-ejp311" @default.
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