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Stochastic Integrals Based on Martingales Taking Values in Hilbert Space

Published online by Cambridge University Press:  22 January 2016

Hiroshi Kunita
Hiroshi Kunita*
Affiliation:
Mathematical Institute, Nagoya University
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Let H be a separable Hilbert space with inner product (,) and norm ║ ║. We denote by K the set of all linear operators on H. Let be a probability space and suppose we are given a family of σ-fields t≥O such that for O ≤ s ≤ t and .

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 38 , March 1970 , pp. 41 - 52
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Daletskii, Yu.L., Infinite-dimensional epllitic operators and parabolic equations connected with them, Uspekhi Mate. Nauk. 22 (1967) (English translation; Russian Math. Surveys)Google Scholar
[2] Kunita, H., and Watanabe, S., On square integrable martingales, Nagoya Math. J. 30 (1967), 209–245.CrossRefGoogle Scholar
[3] Lévy, P., Fonction aleatoires a correlation linaire, Illinois J. Math. 1 (1957), 217–258.Google Scholar
[4] Meyer, P.A., Probability and potentials, Blaisdell, 1966.Google Scholar
[5] Meyer, P.A., Seminaire de probabilites I, Lecture notes in Math., Springer, 1967.Google Scholar