Geodesic
Crossing an Asymptotically Square-Root Boundary by the Brownian Motion
Informatics and Automation, Branching Processes and Related Topics, Tome 316 (2022), pp. 113-128.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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Denis E. Denisov; Günter Hinrichs; Alexander I. Sakhanenko; Vitali I. Wachtel. Crossing an Asymptotically Square-Root Boundary by the Brownian Motion. Informatics and Automation, Branching Processes and Related Topics, Tome 316 (2022), pp. 113-128. http://geodesic.mathdoc.fr/item/TRSPY_2022_316_a8/

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