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2002 Continuous Ocone Martingales as Weak Limits of Rescaled Martingales
Harry Zanten
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Electron. Commun. Probab. 7: 215-222 (2002). DOI: 10.1214/ECP.v7-1062

Abstract

Consider a martingale $M$ with bounded jumps and two sequences $a_n, b_n \to \infty$. We show that if the rescaled martingales $$ M^n_t =\frac{1}{\sqrt{a_n}}M_{b_n t}$$ converge weakly, then the limit is necessarily a continous Ocone martingale. Necessary and sufficient conditions for the weak convergence of the rescaled martingales are also given.

Citation

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Harry Zanten. "Continuous Ocone Martingales as Weak Limits of Rescaled Martingales." Electron. Commun. Probab. 7 215 - 222, 2002. https://doi.org/10.1214/ECP.v7-1062

Information

Accepted: 28 November 2002; Published: 2002
First available in Project Euclid: 16 May 2016

zbMATH: 1017.60053
MathSciNet: MR1952183
Digital Object Identifier: 10.1214/ECP.v7-1062

Subjects:
Primary: 60G44
Secondary: 60F17

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