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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

[1] Al-Hussaini, A. and Elliott, R. J.. The single jump process with some statistical applications. Theory of Probability and Applications. To appear.Google Scholar
[2] Billingsley, P.. Convergence of Probability Measures (J. Wiley, 1968).Google Scholar
[3] Elliott, R. J.. Innovation projections of a jump process and local martingales. Math. Proc. Cambridge Philos. Soc. 81 (1977), 77–90.CrossRefGoogle Scholar
[4] Jacod, J., Klopotowski, A. and Memin, J.. Théorème de la limite centrale et convergence fonctionelle vers un processus à accroissements indépendents: la méthode des martingales. Ann. Inst. H. Poincaré Sect. A 18 (1982), 1–45.Google Scholar
[5] Jacod, J., Memin, J. and Metivier, M.. Stopping times and tightness. Stochastic Process. Appl. 14 (1982), 109–146.CrossRefGoogle Scholar
[6] Lipster, R. and Shiryaev, A.. Statistics of Random Processes, vol. 1 (Springer-Verlag, 1978).Google Scholar