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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 316, Pages 113–128
DOI: https://doi.org/10.4213/tm4241 (Mi tm4241) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Crossing an Asymptotically Square-Root Boundary by the Brownian Motion

Denis E. Denisova, Günter Hinrichsb, Alexander I. Sakhanenkoc, Vitali I. Wachtelb

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
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DOI: https://doi.org/10.4213/tm4241
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.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-12007
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0008
The work of A. Sakhanenko and V. Wachtel was supported by the Russian Foundation for Basic Research and German Research Foundation (DFG), project no. 20-51-12007. The work of A. Sakhanenko was also carried out in part within the framework of the state contract of the Sobolev Institute of Mathematics, project no. 0314-2019-0008.
Received: May 10, 2021
Revised: June 2, 2021
Accepted: November 5, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 316, Pages 105–120
DOI: https://doi.org/10.1134/S0081543822010096
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: Denis E. Denisov, Günter Hinrichs, Alexander I. Sakhanenko, Vitali I. Wachtel, “Crossing an Asymptotically Square-Root Boundary by the Brownian Motion”, Branching Processes and Related Topics, Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin, Trudy Mat. Inst. Steklova, 316, Steklov Math. Inst., Moscow, 2022, 113–128; Proc. Steklov Inst. Math., 316 (2022), 105–120
Citation in format AMSBIB
\Bibitem{DenHinSak22}
\by Denis~E.~Denisov, G\"unter~Hinrichs, Alexander~I.~Sakhanenko, Vitali~I.~Wachtel
\paper Crossing an Asymptotically Square-Root Boundary by the Brownian Motion
\inbook Branching Processes and Related Topics
\bookinfo Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 316
\pages 113--128
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4241}
\crossref{https://doi.org/10.4213/tm4241}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 316
\pages 105--120
\crossref{https://doi.org/10.1134/S0081543822010096}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129048245}
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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