Time inhomogeneity in longest gap and longest run problems
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
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Journal | Stochastic Processes and Their Applications |
Volume | 127 |
Issue number | 2 |
Pages (from-to) | 574-589 |
Number of pages | 16 |
ISSN | 0304-4149 |
DOIs | |
Publication status | Published - 2017 |
Links
- http://arxiv.org/pdf/1510.00579
Submitted manuscript
ID: 162856058