On the tail asymptotics of the area swept under the Brownian storage graph
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| Publication date | 05-2014 |
| Journal | Bernoulli |
| Volume | Issue number | 20 | 2 |
| Pages (from-to) | 395-415 |
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| Abstract |
In this paper, the area swept under the workload graph is analyzed: with {Q(t): t≥0} denoting the stationary workload process, the asymptotic behavior of πT(u)(u):=P(∫T(u)0Q(r)dr>u) is analyzed. Focusing on regulated Brownian motion, first the exact asymptotics of πT(u)(u) are given for the case that T(u) grows slower than u√, and then logarithmic asymptotics for (i) T(u)=Tu√ (relying on sample-path large deviations), and (ii) u√=o(T(u)) but T(u)=o(u). Finally, the Laplace transform of the residual busy period are given in terms of the Airy function. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.3150/12-BEJ491 |
| Downloads |
Arendarczyk_Debicki_Manjdes_Bernoulli_20_2_2014
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