Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T07:39:38.859Z Has data issue: false hasContentIssue false
  • English
  • Français

Innovation projections of a jump process and local martingales

Published online by Cambridge University Press:  24 October 2008

Robert J. Elliott
Robert J. Elliott
Affiliation:
University of Hull
Get access Rights & Permissions [Opens in a new window]

Abstract

Square integrable and local martingales on a family of σ-fields generated by a basic jump process are shown to have representations as stochastic integrals with respect to a family of martingales associated with the jump process by using the idea of an innovation projection and the associated Lévy system, which is a local characterization of the jumps.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 1 , January 1977 , pp. 77 - 90
Copyright
Copyright © Cambridge Philosophical Society 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Chou, C. S. and Meyer, P. A. Sur la représentation des martingales comme intégrales stochastiques dans les processus ponctuels, Séminaire de Probabilités, 1973/1974, Lecture Notes in Mathematics, vol. 465 (Springer Verlag, Heidelberg, 1975).Google Scholar
(2)Clark, J. M. C.The representation of functionals of Brownian motion by stochastic integrals. Ann. Math. Stat. 41 (1970), 1282–1295.CrossRefGoogle Scholar
(3)Davis, M. H. A.The representation of martingales of jump processes, S.I.A.M. J. Control, 14 (1976), 623–638.CrossRefGoogle Scholar
(4)Doleans-Dade, C. and Meyer, P. A. Intégrales Stochastiques par rapport aux martingales locales, Séminaire de Probabilitiés IV, Lecture Notes in Mathematics, vol. 124 (Springer Verlag, Heidelberg, 1970).Google Scholar
(5)Elliott, R. J.Stochastic integrals for martingales of a jump process. Hull University, U.K. preprint.Google Scholar
(6)Elliott, R. J.Martingales of a jump process with partially accessible jump times. Hull University, U.K. preprint.Google Scholar
(7)Kunita, H. and Watanabe, S.On square integrable martingales. Nagoya Math. J. 30 (1967), 209–245.CrossRefGoogle Scholar
(8)Meyer, P. A.Probability and Potentials (Blaisdell, Waltham, Mass., 1966).Google Scholar