Asymptotics of the supremum of scaled Brownian motion

• Autorzy: Dębicki K.
• Języki publikacji: EN

Abstrakty

EN

We consider the problem of estimating the tail of the distribution of the supremum of scaled Brownian motion B(ƒ(t)) processes with linear drift.Using the local time technique we obtain asymptotics and bounds of P_t≥t0(sup(B(ƒ(t))−t)> u), which are expressed in terms of the expected value of thelocal timeof B(ƒ(t))−tprocesses at levelu.As an application we obtain upper bounds for the tail of distribution of the supremum for some Gaussian processes with stationary increments.

Słowa kluczowe

EN

Brownian motion; exponential bound; fractional Brownian motion; Gaussian process; local time; scaled Brownian motion

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 1
• Strony: 199--212
• Opis fizyczny: Biblogr. 14 poz.

Twórcy

autor

Dębicki K.

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

Bibliografia

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