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Accardi L.,Frigerio A., Lewis J.T.: Quantum Stochastic processes, Publications of the R.I.M.S., Kyoto, 18 (1982) 97–133.
Benguria R., Kac M.: Quantum Langevin Equation, Phys. Rev. Lett. 46 (1981) 1–4.
Cramer H.: Stochastic processes as curves in Hilbert space, Theory Prob. Appl. 9 (1964) 169–179.
Doob J.L.: The Brownian movement and stochastic equations, Selected papers on noise and stochastic processes, ed. Nelson Wax, Dover Publications, New York, 1954.
Evans D.E., Lewis J.T.: Dilations of irreversible evolutions in Algebraic Quantum theory, Communications of the Dublin Institute for Advanced studies, Series A, 24 (1977).
Ford G.W., Kac M., Mazur P.: Statistical mechanics of assemblies of coupled oscillators, Journ. Math. Phys. 6 (1965) 504–515.
Frigerio A., Lewis J.T.: Non-Commutative Gaussian Processes, Preprint, Dublin Institute for Advanced Studies, (1980).
Garsia A.M., Rodemich E., Rumsey H.Jr.: A real Variable Lemma and the Continuity of paths of some Gaussian Processes, Indiana University Mathematics Journal 20 (1970) No. 6.
Haag R., Hugenholtz N.M., Winnink M.: On the equilibrium states in quantum statistical mechanics, Comm. Math. Phys. 5 (1967) 215–236.
Kampen N.G. van: Contribution to the quantum theory of light scattering, Mat.-Fys. Medd. Dansk Vid. Selsk. 26 (1951)No. 15.
Kolmogorov A.N.: Curves in Hilbert-space which are invariant with respect to a one-parameter group of motions. DAN SSSR 26 (1940) 6–9.
Lamb H.: Proc. Lond. Math. Soc. 2 (1900) 88.
Langevin P.C.: r. hebd. Séanc. Acad. Sci., Paris, 146 (1908) 530.
Lewis J.T., Puiè j.V.: Dynamical Theories of Brownian Motion, Proceedings International Symposium on Mathematical Problems in Theoretical Physics, ed. H. Araki, 1975. Springer Lecture Notes in Physics 39, 516–519.
Lewis J.T., Thomas L.C. How to make a heat bath, Functional Integration, ed. A.M. Arthurs, Proceedings of International Conference Cumberland Lodge, London, 1974, Oxford, Clarendon Press.
— —: A characterisation of regular solutions of a linear stochastic differential equation, Z.Wahrscheinlichkeitstheorie und verw. Gebiete, 30(1974), 45–55.
— —: On the existence of a class of stationary quantum stochastic processes, Ann. Inst. H. Poincaré Sect. A, 22 (1975) 241–248.
Maassen,H.: On a class of quantum Langevin equations and the question of approach approach to equilibrium, Thesis, Groningen State University, 1982.
Nakazawa: Preprint, Dublin Institute for Advanced Studies, 1983.
Neveu A.: Processus Aléatoires Gaussiens. Faculté de Sciences, Université de Montréal. Publication du Seminaire de Mathématique Supérieure 34 (1968).
Schwabl F., Thirring W.: Quantum Theory of Laser Radiation, Ergebn. Exakten Naturw. 36 (1964) 219–242.
Thomas L.C.: Thesis, Oxford 1971.
Tropper, M.M.: Ergodic and quasideterministic properties of Finite-Dimensional Stochastic Systems, Journ. Stat. Phys. 17 (1977) 491–509.
Uhlenbeck E., Ornstein L.S.: On the theory of the Brownian motion, Phys. Rev. 36 (1930) 823–841.
Wiener N., Paley R.E.A.C.: Am. Mat. Soc. Coll. Publ. Vol. XIX.
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Lewis, J.T., Maassen, H. (1984). Hamiltonian models of classical and quantum stochastic processes. In: Accardi, L., Frigerio, A., Gorini, V. (eds) Quantum Probability and Applications to the Quantum Theory of Irreversible Processes. Lecture Notes in Mathematics, vol 1055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071726
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DOI: https://doi.org/10.1007/BFb0071726
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