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An operator-valued stochastic integral. II. (English) Zbl 0256.60030


MSC:

60H05 Stochastic integrals
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
60J65 Brownian motion
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References:

[1] A.T. Bharucha-Reid , Random Integral Equations , Academic Press , New York (in press). MR 443086 | Zbl 0327.60040 · Zbl 0327.60040
[2] J.L. Doob , Stochastic Processes , John Wiley , New York , 1953 . MR 58896 | Zbl 0053.26802 · Zbl 0053.26802
[3] N. Dunford and J.T. Schwartz , Linear Operators; Part II, Spectral Theory , John Wiley ( Interscience ), New York , 1963 . MR 1009163 | Zbl 0128.34803 · Zbl 0128.34803
[4] P.L. Falb , Infinite dimensional filtering; the Kalman Bucy filter in Hilbert space . Information and Control , vol. 11 , 1967 , p. 102 - 137 . MR 226958 | Zbl 0178.18902 · Zbl 0178.18902 · doi:10.1016/S0019-9958(67)90417-2
[5] E. Hille and R.S. Phillips , Functional Analysis and Semi-groups . Amer. Math. Soc. Colloq. Pub. , vol. 31 , 1957 . MR 89373 | Zbl 0078.10004 · Zbl 0078.10004
[6] K. Itô , On a formula concerning stochastic differentials . Nagoya Math. J. , vol. 3 , 1951 , p. 55 - 65 . Article | MR 44063 | Zbl 0045.07603 · Zbl 0045.07603
[7] D. Kannan and A.T. Bharucha-Reid , An operator-valued stochastic integral , Proc. Japan Acad. , vol. 47 , 1971 , p. 472 - 476 . Article | MR 303604 | Zbl 0256.60029 · Zbl 0256.60029 · doi:10.3792/pja/1195519933
[8] D. Kannan and A.T. Bharucha-Reid , Note on covariance operators of probability measures on a Hilbert space . Proc. Japan Acad. , vol. 46 , 1970 , p. 124 - 129 . Article | MR 283838 | Zbl 0208.43501 · Zbl 0208.43501 · doi:10.3792/pja/1195520454
[9] H. Kunita , Stochastic integrals based on martingales taking values in Hilbert space , Nagoya Math. J. , vol. 38 , 1970 , p. 41 - 52 . Article | MR 264754 | Zbl 0234.60071 · Zbl 0234.60071
[10] P. Levy , Processus stochastiques et mouvement brownien , Gauthier-Villars , Paris , 1948 . MR 190953 | Zbl 0034.22603 · Zbl 0034.22603
[11] R. Schatten , A Theory of Cross-Spaces , Princeton University Press , New Jersey , 1950 . MR 36935 | Zbl 0041.43502 · Zbl 0041.43502
[12] R. Schatten , Norm Ideals of Completely Continuous Operators , Springer-Verlag , 1960 . MR 119112 | Zbl 0090.09402 · Zbl 0090.09402
[13] A.V. Skorokhod , Studies in the theory of Random Processes , Addison-Wesley , Reading, Mass ., 1965 . MR 185620 | Zbl 0146.37701 · Zbl 0146.37701
[14] K. Yoshida , Functional Analysis , Springer-Verlag , 1968 .
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