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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Quasi sure local convergence rate of a Brownian motion in the Hölder norm
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by Yonghong Liu and Yuhui Li PDF
Proc. Amer. Math. Soc. 140 (2012), 715-730 Request permission

Abstract:

We estimate the local convergence rate of Strassen type for a Brownian motion in the Hölder norm with respect to $C_{r,p}$-capacity on an abstract Wiener space. The local convergence rate for increments of a Brownian motion in the Hölder norm with respect to $C_{r,p}$-capacity is also derived.
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Additional Information
  • Yonghong Liu
  • Affiliation: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, People’s Republic of China
  • Email: liuyh1967cn@yahoo.com.cn
  • Yuhui Li
  • Affiliation: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, People’s Republic of China
  • Received by editor(s): December 25, 2009
  • Published electronically: October 5, 2011
  • Additional Notes: The research is supported by the Science Research Foundations for the doctoral program of Guilin University of Electronic Technology under grant UF09007Y and by the Guangxi Natural Science Foundations under grant 2010GXNSB013049
  • Communicated by: Sergei K. Suslov
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 715-730
  • MSC (2010): Primary 60F15, 60F10, 60G17
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11344-3
  • MathSciNet review: 2846341