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August, 1985 Brownian Slow Points: The Critical Case
Burgess Davis, Edwin Perkins
Ann. Probab. 13(3): 779-803 (August, 1985). DOI: 10.1214/aop/1176992908

Abstract

It is known that if $B_t$ is a standard Wiener process then $\sup_t\lim \inf_{h\rightarrow 0+}(B_{t + h} - B_t)h^{-1/2} = 1 a.s.$ Here this is sharpened to $P(\exists t: \lim \inf_{h\rightarrow 0+}(B_{t+h} - B_t)h^{-1/2} = 1) = 1$, and $P(\exists t: B_{t + h} - B_t \geq h^{1/2}\forall h \in (0, \alpha)$ for some $\alpha > 0) = 0$. A number of other theorems of the same flavor are proved. Our results for the critical case for slow points are not as complete as the above.

Citation

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Burgess Davis. Edwin Perkins. "Brownian Slow Points: The Critical Case." Ann. Probab. 13 (3) 779 - 803, August, 1985. https://doi.org/10.1214/aop/1176992908

Information

Published: August, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0576.60030
MathSciNet: MR799422
Digital Object Identifier: 10.1214/aop/1176992908

Subjects:
Primary: 60G17
Secondary: 60G40 , 60J65

Keywords: Brownian motion paths , local properties

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
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