Time inhomogeneity in longest gap and longest run problems

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Standard

Time inhomogeneity in longest gap and longest run problems. / Asmussen, Søren; Ivanovs, Jevgenijs; Rønn-Nielsen, Anders.

In: Stochastic Processes and Their Applications, Vol. 127, No. 2, 2017, p. 574-589.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Asmussen, S, Ivanovs, J & Rønn-Nielsen, A 2017, 'Time inhomogeneity in longest gap and longest run problems', Stochastic Processes and Their Applications, vol. 127, no. 2, pp. 574-589. https://doi.org/10.1016/j.spa.2016.06.018

APA

Asmussen, S., Ivanovs, J., & Rønn-Nielsen, A. (2017). Time inhomogeneity in longest gap and longest run problems. Stochastic Processes and Their Applications, 127(2), 574-589. https://doi.org/10.1016/j.spa.2016.06.018

Vancouver

Asmussen S, Ivanovs J, Rønn-Nielsen A. Time inhomogeneity in longest gap and longest run problems. Stochastic Processes and Their Applications. 2017;127(2):574-589. https://doi.org/10.1016/j.spa.2016.06.018

Author

Asmussen, Søren ; Ivanovs, Jevgenijs ; Rønn-Nielsen, Anders. / Time inhomogeneity in longest gap and longest run problems. In: Stochastic Processes and Their Applications. 2017 ; Vol. 127, No. 2. pp. 574-589.

Bibtex

@article{e996c42ec7674eaf9801b81e7ab5a3da,
title = "Time inhomogeneity in longest gap and longest run problems",
abstract = "Consider an inhomogeneous Poisson process and let D be the first of its epochs which is followed by a gap of size ℓ>0. We establish a criterion for D<∞ a.s., as well as for D being long-tailed and short-tailed, and obtain logarithmic tail asymptotics in various cases. These results are translated into the discrete time framework of independent non-stationary Bernoulli trials where the analogue of DD is the waiting time for the first run of ones of length ℓ A main motivation comes from computer reliability, where D+ℓ represents the actual execution time of a program or transfer of a file of size ℓ in presence of failures (epochs of the process) which necessitate restart.",
author = "S{\o}ren Asmussen and Jevgenijs Ivanovs and Anders R{\o}nn-Nielsen",
year = "2017",
doi = "10.1016/j.spa.2016.06.018",
language = "English",
volume = "127",
pages = "574--589",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier BV * North-Holland",
number = "2",

}

RIS

TY - JOUR

T1 - Time inhomogeneity in longest gap and longest run problems

AU - Asmussen, Søren

AU - Ivanovs, Jevgenijs

AU - Rønn-Nielsen, Anders

PY - 2017

Y1 - 2017

N2 - Consider an inhomogeneous Poisson process and let D be the first of its epochs which is followed by a gap of size ℓ>0. We establish a criterion for D<∞ a.s., as well as for D being long-tailed and short-tailed, and obtain logarithmic tail asymptotics in various cases. These results are translated into the discrete time framework of independent non-stationary Bernoulli trials where the analogue of DD is the waiting time for the first run of ones of length ℓ A main motivation comes from computer reliability, where D+ℓ represents the actual execution time of a program or transfer of a file of size ℓ in presence of failures (epochs of the process) which necessitate restart.

AB - Consider an inhomogeneous Poisson process and let D be the first of its epochs which is followed by a gap of size ℓ>0. We establish a criterion for D<∞ a.s., as well as for D being long-tailed and short-tailed, and obtain logarithmic tail asymptotics in various cases. These results are translated into the discrete time framework of independent non-stationary Bernoulli trials where the analogue of DD is the waiting time for the first run of ones of length ℓ A main motivation comes from computer reliability, where D+ℓ represents the actual execution time of a program or transfer of a file of size ℓ in presence of failures (epochs of the process) which necessitate restart.

U2 - 10.1016/j.spa.2016.06.018

DO - 10.1016/j.spa.2016.06.018

M3 - Journal article

VL - 127

SP - 574

EP - 589

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 2

ER -

ID: 162856058