### Queues, collisions and extremes of integral mean of stationary Gaussian processes

**Debicki, K ***(Wroclaw)*

Tuesday 04 May 2010, 15:00-16:00

Seminar Room 1, Newton Institute

#### Abstract

Let {Z(t):t>0} be a centered stationary Gaussian process with continuous sample paths a.s.
The talk will be focused on the analysis of the asymptotics of P(sup{(1/t)\int_0^t Z(s)ds>u) as u->oo.
As an application of the considered problem, we will derive the exact asymptotics of
- the probability of buffer emptiness for a Gaussian fluid gueue under many-sources regime;
- the probability of a collision of differentiable Gaussian stochastic processes with stationary increments.
The talk is based on a joint work with Kamil Tabi's.

#### Video

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