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