## The Annals of Probability

### 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

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