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October, 1977 Quadratic Variation of Functionals of Brownian Motion
Albert T. Wang
Ann. Probab. 5(5): 756-769 (October, 1977). DOI: 10.1214/aop/1176995717

Abstract

The quadratic variation of functionals $F(t)$ of $n$-dimensional Brownian motion is investigated. Let $\Pi_n = \{t_1^n, t_2^n, \cdots, t^n_{l(n)}\}$ with $a = t_1^n < t_2^n < \cdots < t^n_{l(n)} = b$ be a family of partitions of the interval $\lbrack a, b\rbrack$. The limiting behavior of $Q^2(F, \Pi_n) = \sum^{l(n)-1}_{k=1} (F(t^n_{k+1}) - F(t_k^n))^2$ as $n \rightarrow \infty$, assuming $\|\Pi_n\| \rightarrow 0$, is studied. And the existence of this limit is obtained for a fairly general class of functionals of Brownian motion.

Citation

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Albert T. Wang. "Quadratic Variation of Functionals of Brownian Motion." Ann. Probab. 5 (5) 756 - 769, October, 1977. https://doi.org/10.1214/aop/1176995717

Information

Published: October, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0382.60089
MathSciNet: MR445622
Digital Object Identifier: 10.1214/aop/1176995717

Subjects:
Primary: 60J65
Secondary: 60J55

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • October, 1977
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