Power Law Condition for Stability of Poisson Hail

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Power Law Condition for Stability of Poisson Hail. / Foss, Sergey; Konstantopoulos, Takis; Mountford, Thomas.

In: Journal of Theoretical Probability, Vol. 31, No. 2, 01.06.2018, p. 684-704.

Research output: Contribution to journal › Article › peer-review

Harvard

Foss, S, Konstantopoulos, T & Mountford, T 2018, 'Power Law Condition for Stability of Poisson Hail', Journal of Theoretical Probability, vol. 31, no. 2, pp. 684-704. https://doi.org/10.1007/s10959-016-0723-3

APA

Foss, S., Konstantopoulos, T., & Mountford, T. (2018). Power Law Condition for Stability of Poisson Hail. Journal of Theoretical Probability, 31(2), 684-704. https://doi.org/10.1007/s10959-016-0723-3

Vancouver

Foss S, Konstantopoulos T, Mountford T. Power Law Condition for Stability of Poisson Hail. Journal of Theoretical Probability. 2018 Jun 1;31(2):684-704. doi: 10.1007/s10959-016-0723-3

Author

Foss, Sergey ; Konstantopoulos, Takis ; Mountford, Thomas. / Power Law Condition for Stability of Poisson Hail. In: Journal of Theoretical Probability. 2018 ; Vol. 31, No. 2. pp. 684-704.

BibTeX

@article{1b757b9418dd4dd096341a3068fc510c,

title = "Power Law Condition for Stability of Poisson Hail",

abstract = "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.",

keywords = "Greedy lattice animals, Poisson hail, Stability, Workload",

author = "Sergey Foss and Takis Konstantopoulos and Thomas Mountford",

note = "Publisher Copyright: {\textcopyright} 2016, The Author(s).",

year = "2018",

month = jun,

day = "1",

doi = "10.1007/s10959-016-0723-3",

language = "English",

volume = "31",

pages = "684--704",

journal = "Journal of Theoretical Probability",

issn = "0894-9840",

publisher = "Springer New York",

number = "2",

}

RIS

TY - JOUR

T1 - Power Law Condition for Stability of Poisson Hail

AU - Foss, Sergey

AU - Konstantopoulos, Takis

AU - Mountford, Thomas

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - Greedy lattice animals

KW - Poisson hail

KW - Stability

KW - Workload

UR - http://www.scopus.com/inward/record.url?scp=84996743368&partnerID=8YFLogxK

U2 - 10.1007/s10959-016-0723-3

DO - 10.1007/s10959-016-0723-3

M3 - Article

AN - SCOPUS:84996743368

VL - 31

SP - 684

EP - 704

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 2

ER -

ID: 13488376