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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
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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

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References

REFERENCES

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