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International Journal of Mathematics and Mathematical Sciences
Volume 5, Issue 3, Pages 605-607
http://dx.doi.org/10.1155/S016117128200057X

Square variation of Brownian paths in Banach spaces

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

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is known that if {W(t),0t1} is a standard Brownian motion in then limni=12n|W(i/2n)W((i1)/2n)|2=1 almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces.