Denis E. Denisov, Günter Hinrichs, Alexander I. Sakhanenko, Vitali I. Wachtel, “Crossing an Asymptotically Square-Root Boundary by the Brownian Motion”, Trudy Mat. Inst. Steklova, 2022, Volume 316,Pages <nobr>113

This article is cited in 1 paper

Crossing an Asymptotically Square-Root Boundary by the Brownian Motion

Denis E. Denisov^a, Günter Hinrichs^b, Alexander I. Sakhanenko^c, Vitali I. Wachtel^b

^a Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
^b Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
^c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia

Abstract: We consider first-passage times of the standard Brownian motion over boundaries of order $c\sqrt {t}$. Our main result determines the tail behaviour of such first-passage times. This generalizes the well-known results obtained by Novikov and Uchiyama.

Keywords: Brownian motion, space-time harmonic function, parabolic cylinder function.

UDC: 519.2

Received: May 10, 2021
Revised: June 2, 2021
Accepted: November 5, 2021

DOI: 10.4213/tm4241