Square variation of Brownian paths in Banach spaces

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.

Keywords

• Gaussian measures
• abstract Wiener space
• Brownian motion in Banach spaces
• square variation of Brownian paths.