Quasi sure local convergence rate of a Brownian motion in the Hölder norm
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- by Yonghong Liu and Yuhui Li
- Proc. Amer. Math. Soc. 140 (2012), 715-730
- DOI: https://doi.org/10.1090/S0002-9939-2011-11344-3
- Published electronically: October 5, 2011
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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.References
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Bibliographic 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