SEMINARIESCHEMA FÖR MATEMATISK STATISTIK 

Fredag    31/5  15.15         Krzysztof Dcebicki
          1996                Mathematical Institute,
                              University of Wroclaw:

                              GAUSSIAN FLUID  MODELS



Abstract:

A fluid  model with infinite buffer is considered.
Let Psi(x) be the probability that in steady state
conditions the buffer content exceeds x.
We consider two models:

1) The total net rate  is a stationary Gaussian process with mean
-c and covariance function R(t).
Under condition
\int_0^\infty R(t)\,dt<\infty
we show that Psi(x) le exp[-gamma x] and find gamma.

2) The input is a fractional Brownian motion with Hurst
parameter 0.5 \le H< 1. We show that
Psi(x)\le  C \exp[-alpha x^{2-2H}]+o(exp[-alpha x^{2-2H}])
and find alpha and C.
  
In proofs we use Slepian inequality for Gaussian processes.

This is joint work with Tomasz Rolski.




Lokal: Rum 227 i Mattehuset.

Björn Holmquist 046-2228546