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# A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend

## Titelangaben

Bischoff, Wolfgang ; Hashorva, Enkelejd:
A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend.
In: Statistics & probability letters. 74 (2005). - S. 265-271.
ISSN 0167-7152

## Kurzfassung/Abstract

We show a lower bound for the boundary crossing probability ${\bold P}\{\exists z\in[0,1]$: $h(z)+B_0(z)>u(z)\}$ with $B_0$ a Brownian bridge, $h$ a trend function and $u$ a boundary function. By that we get also a lower bound for the boundary crossing probability ${\bold P}\{\exists z\in[0,1]:h(z)+B_0(z) <u(z)\}$. It turns out that the bound improves the asymptotic result given by the authors, {\it F. Miller} and {\it J Hüsler} [Methodol. Comput. Appl. Probab. 5, 271--287 (2003; Zbl 1048.60025)] when considering a trend function $\gamma h$, $\gamma\to\infty$. The usual tools to obtain boundary crossing probabilities are finite-dimensional approximations of the above probability. However, we use the Cameron-Martin-Girsanov formula to obtain a bound of the above probability.

## Weitere Angaben

Publikationsform: Artikel Brownian bridge with trend; Brownian motion with trend; signal-plus-noise model; Cameron-Martin-Girsanov formula Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Statistik und Stochastik Ja North Holland Publ. Co. Nein 2761
Eingestellt am: 23. Sep 2009 08:26
Letzte Änderung: 28. Jan 2010 11:19
URL zu dieser Anzeige: https://edoc.ku.de/id/eprint/2761/