Matstatseminarium 29.9

Zbigniew Michna
Department of Mathematics, Wroclaw University of Economics, Poland

Bounds and simulation of generalized Pickands constants


Abstract

Generalized Pickands constants appear


in the asymptotic formulas for
the infinite horizon maximum for a stationary
centered Gaussian process
with an added drift term.
In most cases neither explicit nor numerical
approximations are known. In this paper we show
a method of simulation by the use of change of measure technique.
The method is applicablein the case of
a stationary Ornstein-Uhlenbeck


or a more general Gauss-Markov process.
Two examples of simulations are included.
Moreover we give lower bounds for generalized Pickands constants.
(coauthors Krzysztof Debicki and Tomasz Rolski)