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Stochastic differential equations in Hilbert space. (English) Zbl 0225.60028


MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
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References:

[1] Cabana, E., (Stochastic integration in separable Hilbert spaces, IV (1966), Publ. Inst. de Matematica y Estadistica: Publ. Inst. de Matematica y Estadistica Uruguay), 49-79 · Zbl 0154.18702
[2] Curtain, R. F., Stochastic Differential Equations in Hilbert Space, (Thesis (1969), Brown University: Brown University Providence, R. I) · Zbl 0527.93037
[3] Doob, J. L., Stochastic Processes (1953), Wiley and Sons: Wiley and Sons New York · Zbl 0053.26802
[4] Falb, P. L., Infinite dimensional filtering: the Kalman-Bucy filter in Hilbert space, Information and Control, 11, 102-137 (1967) · Zbl 0178.18902
[5] Gikhman, I. I.; Skorokhod, A. V., Introduction to the Theory of Random Processes (1965), Izd-vo “Nauka”: Izd-vo “Nauka” Moscow, (Russ.) · Zbl 0132.37902
[6] Scalora, F. S., Abstract martingale convergence theorems, Pacific J. Math., 11, 347-374 (1961) · Zbl 0114.07702
[7] Skorokhod, A. V., Studies in the Theory of Random Processes (1965), Addison-Wesley: Addison-Wesley Reading, Mass · Zbl 0146.37701
[8] Hille, E.; Phillips, R. S., Functional Analysis and Semigroups (1957), American Mathematical Society: American Mathematical Society Providence, R.J · Zbl 0078.10004
[9] Kato, T., Abstract evolution equations of parabolic type in Banach and Hilbert spaces, Nagoya Math. J., 19, 93-125 (1961) · Zbl 0114.06102
[10] Kato, T.; Tanabe, H., On the abstract evolution equation, Osaka Math. J., 14, 107-133 (1962) · Zbl 0106.09302
[11] H. J. Kushner; H. J. Kushner · Zbl 0186.23404
[12] Lions, J. L., Équations Differentielles, Opérationelles, et Problèmes aux Limites (1961), Springer-Verlag: Springer-Verlag Berlin · Zbl 0098.31101
[13] Phillips, R. S., Perturbation theory for semi-groups of linear operators, Trans. Amer. Math. Soc., 74, 199-221 (1954) · Zbl 0053.08704
[14] Curtain, R. F.; Falb, P. L., Ito’s lemma in infinite dimensions, J. Math. Anal. Appl., 31, 434-448 (1970) · Zbl 0233.60051
[15] Dunford, N.; Schwartz, J. T., Linear Operators. I. General Theory (1958), Interscience: Interscience New York
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