Conditional limit theorems for regulated fractional Brownian motion

Details Conditional limit theorems for regulated fractional Brownian motion Conditional limit theorems for regulated fractional Brownian motion

2009-12-10

arxiv.org/abs/0912.1928v1

Annals of Applied Probability 2009, Vol. 19, No. 6, 2102-2136

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP605 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP605

We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value $b$, we provide the limiting distribution for the amount of time that the workload process spends above level $b$ over the busy cycle straddling the origin, as $b\to\infty$. Our results can be interpreted as showing that long delays occur in large clumps of size of order $b^{2-1/H}$. The conditional limit result involves a finer scaling of the queueing process than fluid analysis, thereby departing from previous related literature.

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