Answers to Some Questions About Increments of a Wiener Process
Guijing, Chen ; Fanchao, Kong ; Zhengyan, Lin
Ann. Probab., Tome 14 (1986) no. 4, p. 1252-1261 / Harvested from Project Euclid
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Let $W(t), 0 \leq t < \infty$, be a Wiener process. This paper proves that $\lim \sup_{T \rightarrow \infty} \sup_{0 < t \leq T} \frac{|W(T) - W(T - t)|}{\{2t(\log(T/t) + \log\log t)\}^{1/2}} = 1, a.s.,$ $\lim_{T \rightarrow \infty} \sup_{0 < t \leq T} \sup_{t \leq s \leq T} \frac{|W(T) - W(s - t)|}{\{2t(\log(T/t) + \log \log t)\}^{1/2}} = 1, a.s.$ These results give an affirmative answer to the questions posed by Hanson and Russo without additional assumptions.
Publié le : 1986-10-14
Classification:  Wiener process,  increments of a Wiener process,  law of iterated logarithm,  almost sure convergence,  60F15,  60G15,  60G17 
@article{1176992366,
     author = {Guijing, Chen and Fanchao, Kong and Zhengyan, Lin},
     title = {Answers to Some Questions About Increments of a Wiener Process},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 1252-1261},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992366}
}

Guijing, Chen; Fanchao, Kong; Zhengyan, Lin. Answers to Some Questions About Increments of a Wiener Process. Ann. Probab., Tome 14 (1986) no. 4, pp.  1252-1261. http://gdmltest.u-ga.fr/item/1176992366/