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

MSC:
60H10Stochastic ordinary differential equations
34F05ODE with randomness
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Full Text: DOI
References:
[1] Cabana, E.: Stochastic integration in separable Hilbert spaces. 4, 49-79 (1966) · Zbl 0154.18702
[2] Curtain, R. F.: Stochastic differential equations in Hilbert space. Thesis (1969)
[3] Doob, J. L.: Stochastic processes. (1953) · 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) · 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) · Zbl 0146.37701
[8] Hille, E.; Phillips, R. S.: Functional analysis and semigroups. (1957) · 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, On the optimal control of a system governed by a linear parabolic equation with ”white noise” inputs, to appear. · Zbl 0186.23404
[12] Lions, J. L.: Équations differentielles, opérationelles, et problèmes aux limites. (1961) · Zbl 0098.31101
[13] Phillips, R. S.: Perturbation theory for semi-groups of linear operators. Trans. amer. Math. soc. 74, 199-221 (1954)
[14] Curtain, R. F.; Falb, P. L.: Itô’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) · Zbl 0084.10402