Square variation of Brownian paths in Banach spaces

Mou-Hsiung Chang

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-3

Abstract:

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

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:284174

DOI: 10.1155/S016117128200057X

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