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.

Saved in:
Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 316; no. 1; pp. 105 - 120
Main Authors Denisov, Denis E., Hinrichs, Günter, Sakhanenko, Alexander I., Wachtel, Vitali I.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2022
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Brownian motion
Mathematics
Mathematics and Statistics
Brownian motion
parabolic cylinder function
space-time harmonic function
Online AccessGet full text

Cover

More Information
Summary: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