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February, 1976 Almost Sure Convergence of the Quadratic Variation of Martingales: A Counterexample
Itrel Monroe
Ann. Probab. 4(1): 133-138 (February, 1976). DOI: 10.1214/aop/1176996192

Abstract

Let $X_s$ be a continuous martingale and $Q\nu$ be an increasing sequence of partitions of [0, 1]. Let $$S^2(Q_\nu) = \sum_{t_i\in Q_\nu} (X_{t_i} - X_{t_{i - 1}})^2.$$ An example is given in which $$\lim \sup_{\nu \rightarrow \infty} S^2(Q_\nu) = \infty.$$

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Itrel Monroe. "Almost Sure Convergence of the Quadratic Variation of Martingales: A Counterexample." Ann. Probab. 4 (1) 133 - 138, February, 1976. https://doi.org/10.1214/aop/1176996192

Information

Published: February, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0336.60048
MathSciNet: MR400384
Digital Object Identifier: 10.1214/aop/1176996192

Subjects:
Primary: 60G45
Secondary: 60J65

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 1 • February, 1976
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