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May, 1985 Local Laws of the Iterated Logarithm for Diffusions
R. F. Bass, K. B. Erickson
Ann. Probab. 13(2): 616-624 (May, 1985). DOI: 10.1214/aop/1176993014


Suppose $X_t$ is a diffusion, reflecting at 0, with speed measure $m(dx)$. We show, under a mild regularity condition on $m$, that $\lim\sup_{t\rightarrow 0} X_t/h^{-1}(t) = c$, a.s., where $c$ is a nonzero constant and $h(t) = tm\lbrack 0, t\rbrack/\log|\log t|$. The analogue to Chung's law of the iterated logarithm is also obtained.


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R. F. Bass. K. B. Erickson. "Local Laws of the Iterated Logarithm for Diffusions." Ann. Probab. 13 (2) 616 - 624, May, 1985.


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

zbMATH: 0567.60077
MathSciNet: MR781428
Digital Object Identifier: 10.1214/aop/1176993014

Primary: 60J60
Secondary: 60F15 , 60J55

Keywords: Additive functionals , Bessel process , Diffusions , Law of the iterated logarithm , Speed measure

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 2 • May, 1985
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