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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Chung’s law for integrated Brownian motion
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by Davar Khoshnevisan and Zhan Shi PDF
Trans. Amer. Math. Soc. 350 (1998), 4253-4264 Request permission


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
  • MR Author ID: 302544
  • Email:
  • Zhan Shi
  • Affiliation: L.S.T.A., Université Paris VI, 4, Place Jussieu, 75252 Paris Cedex 05, France
  • Email:
  • 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
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 4253-4264
  • MSC (1991): Primary 60G15, 60J65; Secondary 60J55
  • DOI:
  • MathSciNet review: 1443196