The Annals of Probability

Local Laws of the Iterated Logarithm for Diffusions

R. F. Bass and K. B. Erickson

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Abstract

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.

Article information

Source
Ann. Probab., Volume 13, Number 2 (1985), 616-624.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993014

Digital Object Identifier
doi:10.1214/aop/1176993014

Mathematical Reviews number (MathSciNet)
MR781428

Zentralblatt MATH identifier
0567.60077

JSTOR
links.jstor.org

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60F15: Strong theorems 60J55: Local time and additive functionals

Keywords
Law of the iterated logarithm diffusions additive functionals speed measure Bessel process

Citation

Bass, R. F.; Erickson, K. B. Local Laws of the Iterated Logarithm for Diffusions. Ann. Probab. 13 (1985), no. 2, 616--624. doi:10.1214/aop/1176993014. https://projecteuclid.org/euclid.aop/1176993014


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Corrections

  • See Correction: R. F. Bass, K. B. Erickson. Correction: Local Laws of the Iterated Logarithm for Diffusions. Ann. Probab., Volume 14, Number 2 (1986), 731--731.