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Semimartingales and the empirical distribution

Published online by Cambridge University Press:  24 October 2008

Ata N. Al-Hussaini  and
Robert J. Elliott
Ata N. Al-Hussaini
Affiliation:
Department of Statistics and Applied Probability, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1
Robert J. Elliott
Affiliation:
Department of Pure Mathematics, University of Hull, Hull, England Hu6 7RX
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Abstract

Processes related to the empirical distribution are shown to converge to a time changed Brownian motion. In particular, the time change of the Brownian motion differs from the time change obtained by using the distribution function: this gives rise to two different representations of a related Brownian bridge.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 1 , July 1984 , pp. 167 - 171
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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