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Power Law Condition for Stability of Poisson Hail
Heriot Watt Univ, Sch Math & Comp Sci, Edinburgh EH14 4AS, Midlothian, Scotland;Sobolev Inst Math, Novosibirsk, Russia;Novosibirsk State Univ, Novosibirsk, Russia.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Ecole Polytech Fed Lausanne, Inst Math, Stn 8, CH-1015 Lausanne, Switzerland.
2018 (English)In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 31, no 2, p. 684-704Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
SPRINGER/PLENUM PUBLISHERS , 2018. Vol. 31, no 2, p. 684-704
Keywords [en]
Poisson hail, Stability, Workload, Greedy lattice animals
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-356626DOI: 10.1007/s10959-016-0723-3ISI: 000432743300003OAI: oai:DiVA.org:uu-356626DiVA, id: diva2:1236496
Funder
Swedish Research Council, 2013-4688Available from: 2018-08-02 Created: 2018-08-02 Last updated: 2018-08-02Bibliographically approved

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