Search results for "Galton–Watson process"

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A Galton–Watson process with a threshold

2016

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.

Statistics and ProbabilityGeneral MathematicsPopulation size010102 general mathematicsMean valueProcess (computing)01 natural sciencesGalton–Watson processBranching (linguistics)010104 statistics & probabilityIntegerStatistical physics0101 mathematicsStatistics Probability and UncertaintyFinite timeMathematicsBranching processJournal of Applied Probability
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Hitting straight lines by compound Poisson process paths

1990

In a recent article Mallows and Nair (1989,Ann. Inst. Statist. Math.,41, 1–8) determined the probability of intersectionP{X(t)=αt for somet≥0} between a compound Poisson process {X(t), t≥0} and a straight line through the origin. Using four different approaches (direct probabilistic, via differential equations and via Laplace transforms) we extend their results to obtain the probability of intersection between {X(t), t≥0} and arbitrary lines. Also, we display a relationship with the theory of Galton-Watson processes. Additional results concern the intersections with two (or more) parallel lines.

Statistics and ProbabilityLaplace transformDifferential equationMathematical analysisProbabilistic logicPoisson processParallelGalton–Watson processCombinatoricssymbols.namesakeIntersectionCompound Poisson processsymbolsMathematicsAnnals of the Institute of Statistical Mathematics
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