6533b870fe1ef96bd12cfaca

RESEARCH PRODUCT

A Galton–Watson process with a threshold

Krishna B. AthreyaH. J. Schuh

subject

Statistics and ProbabilityGeneral MathematicsPopulation size010102 general mathematicsMean valueProcess (computing)01 natural sciencesGalton–Watson processBranching (linguistics)010104 statistics & probabilityIntegerStatistical physics0101 mathematicsStatistics Probability and UncertaintyFinite timeMathematicsBranching process

description

Abstract In this paper we study a special class of size dependent branching processes. We assume that for some positive integer K as long as the population size does not exceed level K, the process evolves as a discrete-time supercritical branching process, and when the population size exceeds level K, it evolves as a subcritical or critical branching process. It is shown that this process does die out in finite time T. The question of when the mean value E(T) is finite or infinite is also addressed.

yearjournalcountryeditionlanguage
2016-06-01Journal of Applied Probability
https://doi.org/10.1017/jpr.2016.26