How many families survive for a long time
V.A. Vatutin, E.E. Dyakonova

TL;DR
This paper analyzes the long-term survival probabilities of families in a critical branching process within a random environment, providing a theorem on the limiting distribution of the scaled logarithm of the process.
Contribution
It introduces a new theorem describing the asymptotic behavior of the process's logarithm in critical branching processes with random environments.
Findings
Limiting distribution of scaled log process derived
Conditions for long-term family survival established
Asymptotic behavior characterized as n approaches infinity
Abstract
A critical branching process in a random environment generated by a sequence of independent and identically distributed random reproduction laws is considered.\ Let be the number of particles at time having a positive offspring number at time . \ A theorem is proved describing the limiting behavior, as of the distribution of a properly scaled process under the assumptions and .
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Taxonomy
TopicsStochastic processes and statistical mechanics · Probability and Risk Models · Bayesian Methods and Mixture Models
