Open Access
July, 1989 Some "LIM INF" Results for Increments of a Wiener Process
D. L. Hanson, Ralph P. Russo
Ann. Probab. 17(3): 1063-1082 (July, 1989). DOI: 10.1214/aop/1176991257


Let $W(t)$ for $0 \leq t < \infty$ be a standard Wiener process, suppose $0 < a_T \leq T$ for $T > 0$, and let $d(T, t) = \{2t\lbrack\log(T/t) + \log \log t \rbrack\}^{1/2}$. Quantities such as $\lim, \inf_{T \rightarrow \infty} \sup_{a_T \leq t \leq T} \frac{W(T) - W(T - t)}{d(T,t)},$ $\lim, \inf_{T \rightarrow \infty} \sup_{\substack{0 \leq t \leq T - a_T\\0 \leq s \leq a_T}} \frac{|W(t + s) - W(t)|}{d(t + a_T, a_T)}$ and $\lim, \inf_{T \rightarrow \infty} \sup_{\substack{0 \leq u < v \leq T\\a_T \leq v - u}} \frac{|W(v) - W(u)|}{d(v, v - u)}$ are investigated.


Download Citation

D. L. Hanson. Ralph P. Russo. "Some "LIM INF" Results for Increments of a Wiener Process." Ann. Probab. 17 (3) 1063 - 1082, July, 1989.


Published: July, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0684.60021
MathSciNet: MR1009445
Digital Object Identifier: 10.1214/aop/1176991257

Primary: 60F15
Secondary: 60G15 , 60G17

Keywords: Increments of a Wiener process , Wiener process

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 3 • July, 1989
Back to Top