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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 605-607
doi:10.1155/S016117128200057X

Square variation of Brownian paths in Banach spaces

Mou-Hsiung Chang

Department of Mathematics, University of Alabama in Huntsville, Huntsville 35899, Alabama, USA

Abstract

It is known that if {W(t), 0≤t≤1} is a standard Brownian motion in ℝ then limn→∞∑i=12n|W(i/2n)−W((i−1)/2n)|2=1 almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces.