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

60H10Stochastic ordinary differential equations
34F05ODE with randomness
Full Text: DOI
[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
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[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