Crossing an Asymptotically Square-Root Boundary by the Brownian Motion

Crossing an Asymptotically Square-Root Boundary by the Brownian Motion

We consider first-passage times of the standard Brownian motion over boundaries of order . Our main result determines the tail behaviour of such first-passage times. This generalizes the well-known results obtained by Novikov and Uchiyama.

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Veröffentlicht in:Proceedings of the Steklov Institute of Mathematics 2022-03, Vol.316 (1), p.105-120
Hauptverfasser: Denisov, Denis E., Hinrichs, Günter, Sakhanenko, Alexander I., Wachtel, Vitali I.
Format: Artikel
Sprache:eng
Schlagworte:
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Brownian motion
Mathematics
Mathematics and Statistics
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Beschreibung
Zusammenfassung:We consider first-passage times of the standard Brownian motion over boundaries of order . Our main result determines the tail behaviour of such first-passage times. This generalizes the well-known results obtained by Novikov and Uchiyama.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543822010096