## The Annals of Probability

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

### Local Laws of the Iterated Logarithm for Diffusions

#### 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

#### 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.Project Euclid: euclid.aop/1176992542