Criticality for branching processes in random environment

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dc.creatorAfanasyev, V. I.
dc.creatorGeiger, J.
dc.creatorKersting, G.
dc.creatorVatutin, V. A.
dc.date2005-03-29
dc.date.accessioned2026-07-07T05:18:35Z
dc.date.available2026-07-07T05:18:35Z
dc.descriptionWe study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching processes are developed under a general assumption, known as Spitzer's condition in fluctuation theory of random walks, and some additional moment condition. We determine the exact asymptotic behavior of the survival probability and prove conditional functional limit theorems for the generation size process and the associated random walk. The results rely on a stimulating interplay between branching process theory and fluctuation theory of random walks.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117904000000928 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503657
dc.identifierhttp://arxiv.org/abs/math/0503657
dc.identifierAnnals of Probability 2005, Vol. 33, No. 2, 645-673
dc.identifierdoi:10.1214/009117904000000928
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74713
dc.subjectProbability
dc.subject60J80 (Primary) 60G50, 60F17. (Secondary)
dc.titleCriticality for branching processes in random environment
dc.typetext

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