References
Berman, N., Root, W.L.: A weak stochastic integral in Banach space with application to a linear stochastic differential equation. Appl. Math. Optim.10, 97–125 (1983)
Bourbaki, N.: Topologie générale. Paris: Hermann 1974
Curtain, R.F.: Stochastic evolution equations with general white noise disturbance. J. Math. Anal. Appl.60, 570–595 (1977)
Curtain, R.F.: Linear stochastic Itô equations in Hilbert space. Lecture Notes in Control and Information Sciences, Vol. 16, pp. 61–84. Berlin, Heidelberg, New York: Springer 1979
Curtain, R.F.: Markov processes generated by linear stochastic evolution equations. Stochastics5, 135–165 (1981)
Curtain, R.F., Falb, P.L.: Stochastic differential equations in Hilbert spaces. J. Differential Equations10, 412–430 (1971)
Curtain, R.F., Pritchard, A.J.: Infinite dimensional linear systems theory. Lecture Notes in Control and Information Sciences, Vol. 8. Berlin, Heidelberg, New York: Springer 1978
Da Prato, D., Ianelli, M., Tubaro, L.: Semi-linear stochastic differential equations in Hilbert spaces. Boll. UMI16 A, 168–185 (1979)
Dieudonné, J.: Foundations of modern analysis. New York, London: Academic Press 1969
Doss, H., Royer, G.: Processus de diffusion associé aux mesures de Gibbs sur\(\mathbb{R}^{\mathbb{Z}^d } \). Z. Wahrscheinlichkeitstheorie u. verw. Gebiete46, 125–158 (1979)
Ibragimov, I.A., Rozanov, Y.A.: Gaussian random processes. Berlin, Heidelberg, New York: Springer 1978
Leha, G., Ritter, G.: On diffusion processes and their semi-groups in Hilbert spaces with an application to interacting stochastic systems. Ann. Probability (to appear)
Métivier, M.: Semimartingales. Studies in Mathematics 2. Berlin, New York: de Gruyter 1982
Métivier, M., Pistone, G.: Sur une équation d'évolution stochastique. Bull. Soc. math. France104, 65–85 (1976)
Nelson, E.: Probability theory and Euclidean field theory. Lecture Notes in Physics, Vol. 25, pp. 94–124. Berlin, Heidelberg, New York: Springer 1979
Shiga, T., Shimizu, A.: Infinite dimensional differential equations and their applications. J. Math. Kyoto Univ.20, 395–416 (1980)
Stroock, D.W., Varadhan, S.R.S.: Multidimensional diffusion processes. Berlin, Heidelberg, New York: Springer 1979
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Leha, G., Ritter, G. On solutions to stochastic differential equations with discontinuous drift in Hilbert space. Math. Ann. 270, 109–123 (1985). https://doi.org/10.1007/BF01455536
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DOI: https://doi.org/10.1007/BF01455536