On the supremum from gaussian processes over infinite horizon

• Autorzy: Dębicki Krzysztof , Michna Zbigniew , Rolski Tomasz
• Języki publikacji: EN

Abstrakty

EN

In the paper we study the asymptotic of the tail of distribution function P(A(X,c) > x) for x→∞, where A(X, c) is the supremum of X (t)—ct over [0, ∞). 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].

Słowa kluczowe

EN

gaussian processes; asymptotic of the tail; fractional Brownian motion

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1998
• Tom: Vol. 18, Fasc. 1
• Strony: 83--100
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Dębicki Krzysztof

• Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Michna Zbigniew

• Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden

autor

Rolski Tomasz

• Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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