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Convergent processes, projective systems of measures and martingale decompositions

Published online by Cambridge University Press:  18 May 2009

Louis H. Blake
Louis H. Blake
Affiliation:
Department of Mathematics, College of Staten Island, Cuny, Staten Island, New York 10301.
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The purpose of this paper is to show the equivalence of convergence, an associated projective system of measures and a martingale decomposition for a uniformly integrable stochastic process. Emphasis is placed on a direct juxtaposition of these concepts and on displaying underlying mechanisms.

The impact of the martingale convergence theorem on contemporary probability theory has been immense. Therein lies the reason for numerous generalizations of both the basic martingale convergence theorem and the martingale concept itself.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 20 , Issue 2 , July 1979 , pp. 119 - 124
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

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