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On Square Integrable Martingales

Published online by Cambridge University Press:  22 January 2016

Hiroshi Kunita  and
Shinzo Watanabe
Hiroshi Kunita
Affiliation:
University of Illinois, Nagoya University and Stanford University, Kyoto University
Shinzo Watanabe
Affiliation:
University of Illinois, Nagoya University and Stanford University, Kyoto University
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Theory of real and time continuous martingales has been developed recently by P. Meyer [8, 9]. Let be a square integrable martingale on a probability space P. He showed that there exists an increasing process ‹X›t such that

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 209 - 245
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Courrège, P., Intégrales stochastiques et martingales de carré integrable, Seminaire Breîot-Choquet-Deny 7e annee (1962/63) 7.Google Scholar
[2] Doob, J.L., Stochastic processes, New York (1953).Google Scholar
[3] Dubins, L.E., Schwarz, G., On continuous martingales, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 913–916.CrossRefGoogle ScholarPubMed
[4] Itô, K., Lectures on stochastic processes, Tata Institute of Fundamental Research, Bombay (1961).Google Scholar
[5] Itô, K., Watanabe, S., Transformation of Markov process by multiplicative functional, Ann. Inst. Fourier, Grenoble 15 (1965), 13–30.CrossRefGoogle Scholar
[6] Kunita, H., T Watanabe, Notes on transformations of Markov processes connected with multiplicative functionals, Mem. Fac. Sci. Kyushu Univ. 17 (1963), 181–191.Google Scholar
[7] Levy, P., Theorie de l’addition des variables aleatoires, Paris (1937).Google Scholar
[8] Meyer, P.A., A decomposition theorem for supermartingales, Illinois J. Math. 6 (1962), 193–205.CrossRefGoogle Scholar
[9] Meyer, P.A., Decompositions of supermartingales; The uniqueness theorem, Illinois J. Math. 7 (1963), 1–17.CrossRefGoogle Scholar
[10] Motoo, M., Watanabe, S., On a class of additive functionals of Markov process, J. Math. Kyoto Univ. 4 (1965), 429–469.Google Scholar
[11] Watanabe, S., On discontinuous additive functionals and Levy measures of a Markov process, Japanese J. Math. 36 (1964), 53–70.CrossRefGoogle Scholar
[12] Wentzel, A.D., Additive functionals of multidimensional Wiener process, D.A.N. SSSR, 139 (1961), 13–16.Google Scholar