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- W2051482788 abstract "1. Let X(t) be standard Brownian motion on [0, 1], P a finite partition of [0, 1], and 1P a collection of such partitions. Denote Zti p I X(t)-X(ti1) I 2 by var (X, P). P. Levy has shown [2 ] that if aP is a fixed increasing sequence of partitions Pn which becomes dense in [0, 1], then with probability one, lim_O var(X, Pn) = 1; whereas if 6 is all finite partitions with probability one, supp,,p var(X, P) = oo. For fixed n, let (9' be all partitions containing at most n points. Since almost all sample paths are continuous, suppE:p'n var(X, P) 1/n. Then (P. is a subset of Pn, and for a sample path X," @default.
- W2051482788 created "2016-06-24" @default.
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- W2051482788 date "1969-01-01" @default.
- W2051482788 modified "2023-09-24" @default.
- W2051482788 title "An asymptotic estimate of Brownian path variation" @default.
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- W2051482788 doi "https://doi.org/10.1090/s0002-9939-1969-0235617-3" @default.
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