Sample path properties of reflected Gaussian processes

Abstract

We consider a stationary queueing process $Q_X$ fed by a centered Gaussian process $X$ with stationary increments and variance function satisfying classical regularity conditions. A criterion when, for a given function $f$, $\mathbb{P}(Q_X(t)>f(t)\text{ i.o.})$ equals 0 or 1 is provided. Furthermore, an Erdös-Révész type law of the iterated logarithm is proven for the last passage time $\xi (t)=\sup \{s:0\le s\le t,Q_X(s)\ge f(s)\}$. Both of these findings extend previously known results that were only available for the case when $X$ is a fractional Brownian motion.

arXiv admin note: substantial text overlap with arXiv:1612.09229

References in corpus (3)

• On the infimum attained by the reflected fractional Brownian motion
• An Erdös--Révész type law of the iterated logarithm for order statistics of a stationary Gaussian process
• An Erdös-Révész type law of the iterated logarithm for reflected fractional Brownian motion