Power Law Condition for Stability of Poisson Hail

Sergey Foss, Takis Konstantopoulos, Thomas Mountford

Результат исследования: Научные публикации в периодических изданияхстатья

1 Цитирования (Scopus)

Аннотация

The Poisson hail model is a space-time stochastic system introduced by Baccelli and Foss (J Appl Prob 48A:343–366, 2011) whose stability condition is nonobvious owing to the fact that it is spatially infinite. Hailstones arrive at random points of time and are placed in random positions of space. Upon arrival, if not prevented by previously accumulated stones, a stone starts melting at unit rate. When the stone sizes have exponential tails, then stability conditions exist. In this paper, we look at heavy tailed stone sizes and prove that the system can be stabilized when the rate of arrivals is sufficiently small. We also show that the stability condition is, in a weak sense, optimal. We use techniques and ideas from greedy lattice animals.

Язык оригиналаанглийский
Страницы (с-по)684-704
Число страниц21
ЖурналJournal of Theoretical Probability
Том31
Номер выпуска2
DOI
СостояниеОпубликовано - 1 июн 2018

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