# Conditional limit theorems for regulated fractional Brownian motion - Mathematics > Probability

Conditional limit theorems for regulated fractional Brownian motion - Mathematics > Probability - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: 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 workloadprocess 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 occurin large clumps of size of order $b^{2-1-H}$. The conditional limit resultinvolves a finer scaling of the queueing process than fluid analysis, therebydeparting from previous related literature.