Square variation of Brownian paths in Banach spaces
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.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117128200057X |
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