Sample path properties of reflected Gaussian processes
Details
Serval ID
serval:BIB_E274DCA898D3
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Sample path properties of reflected Gaussian processes
Journal
Latin American Journal of Probability and Mathematical Statistics
ISSN
1980-0436
Publication state
Published
Issued date
2018
Peer-reviewed
Oui
Volume
15
Number
1
Pages
453
Language
english
Abstract
We consider a stationary queueing process QX fed by a centered Gaussian process X with stationary increments and variance function satisfying classical regularity conditions. A criterion when, for a given function f, P(QX(t) > f(t) i.o.) equals 0 or 1 is provided. Furthermore, an Erdös–Révész type law of the iterated logarithm is proven for the last passage time ξ(t) = sup{s : 0 ≤ s ≤ t, QX(s) ≥ f(s)}. Both of these findings extend previously known results that were only available for the case when X is a fractional Brownian motion.
Keywords
Statistics and Probability, Statistics and Probability
Open Access
Yes
Create date
28/04/2018 19:32
Last modification date
20/08/2019 17:06