Geodesic
Some Results on Increments of the Wiener Process
Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 2 
A. Bahram. Some Results on Increments of the Wiener Process. Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2005_74_2_a1/
@article{AMUC_2005_74_2_a1,
     author = {A. Bahram},
     title = {Some {Results} on {Increments} of the {Wiener} {Process}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2005},
     volume = {74},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2005_74_2_a1/}
}
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Let <span class="cmmi-10"> l ( T,a T ,a ) = alt="{ [ -T ]} 2aT logaT + aloglogT + (1 - a)log logaT" class="left" align="middle"> -1/2 where 0 < <span class="cmmi-10"> a <img src="cmmi10-b.gif" alt="a" class="10x-x-b"> < 1 and <img src="bah2x.gif" alt=" { W ( t ), t > 0} " class="left" align="middle"> be a standard Wiener process. This paper studies the almost sure limiting behaviour of sup 0<t<T-aT <span class="cmmi-10"><img src="cmmi10-15.gif" alt="c" class="10x-x-15"></span> l ( T,a T ,a ) <sub > <span class="cmr-7">(</span><span class="cmmi-7">T,a</span><sub ><span class="cmmi-5">T</span></sub><span class="cmmi-7">,<img src="cmmi7-b.gif" alt="a" class="7x-x-b"></span><span class="cmr-7">)</span></sub> | W ( t + a T ) – W ( t ) | as T ® ¥ under varying conditions on aT and T/aT . Keywords: Wiener process, increments of a Wiener process, a law of the iterated logarithm. AMS Subject classification: 60J65. Download: Adobe PDF Compressed Postscript Version to read: Adobe PDF Acta Mathematica Universitatis Comenianae Institute of Applied Mathematics Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295755 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © Copyright 2005, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE