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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 18, Fasc. 1,
pages 83 - 100
 

ON THE SUPREMUM FROM GAUSSIAN PROCESSES OVER INFINITE HORIZON

Krzysztof Dębicki
Zbigniew Michna
Tomasz Rolski

Abstract: In the paper we study the asymptotic of the tail of distribution function P (A(X, c) > x) for x --> oo , where A(X, c) is the supremum of X(t)- ct over [0, oo ). In particular, X(t) is the fractional Brownian motion, a nonlinearly scaled Brownian motion or some integrated stationary Gaussian processes. For the fractional Brownian motion we give a stronger result than a recent one of Duffield and O’Connell [5].

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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