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A note on stochastic integrators

Published online by Cambridge University Press:  24 October 2008

D. A. Edwards
D. A. Edwards
Affiliation:
Mathematical Institute, 24–29 St Giles, Oxford
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Extract

The object of this paper is to show that some important classes of stochastic processes can be proved to be stochastic integrators, in the sense of Bichteler[1], by entirely elementary methods. Let us recall what this means.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 395 - 400
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Bichteler, K.. Stochastic integration and L p-theory of semimartingales. Ann. Probab. 9 (1981), 49–89.CrossRefGoogle Scholar
[2]Burkholder, D. L.. Martingale transforms. Ann. Math. Statist. 37 (1966), 1494–1504.CrossRefGoogle Scholar
[3]Dellacherie, C.. Un survol de la théorie de l'intégrale stochastique. Stochastic Process. Appl. 10 (1980), 115–144.CrossRefGoogle Scholar
[4]Dellacherie, C. and Meyer, P.-A.. Probabilitiés et Potentiel, Chapitres V–VIII (Hermann, 1980).Google Scholar
[5]Meyer, P.-A.. Martingales and Stochastic Integrals. Lecture Notes in Math. vol. 284 (Springer-Verlag, 1972).CrossRefGoogle Scholar
[6]Meyer, P.-A.. Caractérisation des semimartingales, d'après Dellacherie. In Séminaire Probabilités XIII, Lecture Notes in Math. vol. 721 (Springer-Verlag, 1979). pp. 620–623.CrossRefGoogle Scholar
[7]Neveu, J.. Martingales à Temps Discret (Masson, 1972).Google Scholar
[8]Rao, K. M.. Quasimartingales. Math. Scand. 24 (1969), 79–92.CrossRefGoogle Scholar
[9]Rao, M. M.. Doob's decomposition and Burkholder's inequalities. In Séminaire Probabilités VI, Lecture Notes in Math. vol. 258 (Springer-Verlag, 1972). pp. 198–201.Google Scholar
[10]Rogers, L. C. G. and Williams, D.. Diffusions, Markov Processes and Martingales, vol. 2 (Wiley, 1987).Google Scholar
[11]Stricker, C.. Quasimartingales, martingales locales, semimartingales et filtrations naturelles. Z. Wahrsch. Verw. Gebiete 39 (1977), 55–64.CrossRefGoogle Scholar