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October, 1976 A Criterion for Tightness for a Sequence of Martingales
R. M. Loynes
Ann. Probab. 4(5): 859-862 (October, 1976). DOI: 10.1214/aop/1176995990

Abstract

An improved result is presented, showing that if the finite-dimensional distributions of a sequence of martingales converge, and if for each time $t$ the variables are uniformly integrable, then weak convergence follows (in either $C$ or $D$) provided the limiting process satisfies a certain condition; this condition is satisfied by the Wiener process.

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R. M. Loynes. "A Criterion for Tightness for a Sequence of Martingales." Ann. Probab. 4 (5) 859 - 862, October, 1976. https://doi.org/10.1214/aop/1176995990

Information

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

zbMATH: 0336.60007
MathSciNet: MR433536
Digital Object Identifier: 10.1214/aop/1176995990

Subjects:
Primary: 60B10
Secondary: 60F05, 60G45

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 5 • October, 1976
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