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Chung's law for integrated Brownian motion


Authors: Davar Khoshnevisan and Zhan Shi
Journal: Trans. Amer. Math. Soc. 350 (1998), 4253-4264
MSC (1991): Primary 60G15, 60J65; Secondary 60J55
DOI: https://doi.org/10.1090/S0002-9947-98-02011-X
MathSciNet review: 1443196
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Abstract: The small ball problem for the integrated process of a real-valued Brownian motion is solved. In sharp contrast to more standard methods, our approach relies on the sample path properties of Brownian motion together with facts about local times and Lévy processes.


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Additional Information

Davar Khoshnevisan
Affiliation: Department of Mathematics, Univeristy of Utah, Salt Lake City, Utah 82112
Email: davar@math.utah.edu

Zhan Shi
Affiliation: L.S.T.A., Université Paris VI, 4, Place Jussieu, 75252 Paris Cedex 05, France
Email: shi@ccr.jussieu.fr

DOI: https://doi.org/10.1090/S0002-9947-98-02011-X
Keywords: Small ball probability, integrated Brownian motion
Received by editor(s): October 19, 1996
Received by editor(s) in revised form: January 3, 1997
Additional Notes: Research partially supported by grants from the National Science Foundation and the National Security Agency
Article copyright: © Copyright 1998 American Mathematical Society