Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory
Annales de l'I.H.P. Probabilités et statistiques, Volume 31 (1995) no. 4, p. 601-651
@article{AIHPB_1995__31_4_601_0,
author = {Rajarama Bhat, B. V. and Parthasarathy, Kalyanapuram Rangachari},
title = {Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
publisher = {Gauthier-Villars},
volume = {31},
number = {4},
year = {1995},
pages = {601-651},
zbl = {0832.46060},
mrnumber = {1355610},
language = {en},
url = {http://www.numdam.org/item/AIHPB_1995__31_4_601_0}
}

Rajarama Bhat, B. V.; Parthasarathy, K. R. Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory. Annales de l'I.H.P. Probabilités et statistiques, Volume 31 (1995) no. 4, pp. 601-651. http://www.numdam.org/item/AIHPB_1995__31_4_601_0/

[AFL] L. Accardi, A. Frigerio and J.T. Lewis, Quantum stochastic processes, Proc. Res. Inst. Math. Sci., Kyoto, Vol. 18, 1982, pp. 97-133. | MR 660823 | Zbl 0498.60099

[B] B.V.R. Bhat, Markov Dilations of Nonconservative Quantum Dynamical Semigroups and a Quantum Boundary Theory, Ph. D. Thesis, Indian Statistical Institute, Delhi Centre, 1993.

[BP] B.V.R. Bhat and K.R. Parthasarathy, Kolmogorov's existence theorem for Markov processes in C* algebras, Proc. Ind. Acad. Sci. (Mathematical Sciences), Vol. 104, 1994, pp. 253-262. | MR 1280073 | Zbl 0796.60092

[C1] K.L. Chung, Markov Chains with Stationary Transition Probabilities, Springer, Berlin, Gottingen. Heidelberg, 1960. | MR 116388 | Zbl 0092.34304

[C2] K.L. Chung, Lectures on the Boundary Theory for Markov Chains, Princeton University Press, 1970. | MR 267644 | Zbl 0204.51003

[CW] K.L. Chung and R.J. Williams, Introduction to Stochastic Integration, Birkhäuser, Boston. Basil. Stuttgart, 1983. | MR 711774 | Zbl 0527.60058

[Da] E.B. Davies, Quantum dynamical semigroups and the neutron diffusion equation, Rep. Math. Phys., Vol. 11, 1977, pp. 169-189. | MR 503331 | Zbl 0372.47020

[Dy] E.B. Dynkin, Markov Processes, Vol. I and II, Springer-Verlag, Berlin. Gottingen. Heidelberg, 1965. | MR 193671 | Zbl 0132.37901

[EL] D.E. Evans and J.T. Lewis, Dilations of Irreducible Evolutions in Algebraic Quantum Theory, Communications of the Dublin Institute for Advanced Studies, Series A (Theoretical Physics), No. 24, Dublin, 1977. | Zbl 0365.46059

[Em] G.G. Emch, Minimal dilations of CP flows, C* algebras and applications to physics, Springer LNM 650, 1978, pp. 156-159. | MR 504761 | Zbl 0385.46035

[Fa] F. Fagnola, Unitarity of solutions to quantum stochastic differential equations and conservativity of the associated semigroups, in Quantum Probability and Related Topics, Vol. VII, 1992, pp. 139-148 (World Scientific, River Edge NJ). | MR 1186660 | Zbl 0789.47027

[Fe1] W. Feller, Boundaries induced by non-negative matrices, Trans. of the Amer. Math. Soc., Vol. 83, No. 1, 1956, pp. 19-54. | MR 90927 | Zbl 0071.34901

[Fe2] W. Feller, On boundaries and lateral conditions for the Kolmogorov differential equations, Annals of Mathematics, Vol. 65, No. 3, 1957, pp. 527-70. | MR 90928 | Zbl 0084.35503

[Fe3] W. Feller, Notes to my paper "On boundaries and lateral conditions for the Kolmogorov differential equations", Annals of Mathematics, Vol. 68, No. 3, 1958, pp. 735-736. | MR 106508 | Zbl 0084.35503

[H] R.L. Hudson, The strong Markov property for canonical Wiener processes, J. Func. Anal., Vol. 34, 1979, pp. 266-281. | MR 552705 | Zbl 0424.46048

[HIP] R.L. Hudson, P.D.F. Ion and K.R. Parthasarathy, Time-orthogonal unitary dilations and non-commutative Feynman-Kac formulae, Commun. Math. Phys., Vol. 83, 1982, pp. 261-280. | MR 649162 | Zbl 0485.46038

[Me] P.A. Meyer, Quantum Probability for Probabilists, LNM 1538, Springer Verlag, 1993. | MR 1222649 | Zbl 0773.60098

[Mo] A. Mohari, Quantum Stochastic Calculus with Infinite Degrees of Freedom and Its Applications, Ph. D. Thesis, Indian Statistical Institute, Delhi Centre, New Delhi, 1991.

[P1] K.R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Monographs in Mathematics, Birkhauser Verlag, Basil, 1991. | Zbl 0751.60046

[P2] K.R. Parthasarathy, A continuous time version of Stinespring's theorem on completely positive maps, in Quantum Probability and Applications V, L. Accardi, W.Von Walden-fels (Eds.), Lecture Notes in Mathematics, 1442, Springer-Verlag, Heidelberg, 1990, pp. 296-300. | Zbl 0743.46060

[PS] K.R. Parthasarathy and K.B. Sinha, Stoptimes in Fock space stochastic calculus, Probab. Th. Rel. Fields, Vol. 75, 1987, pp. 317-349. | MR 890283 | Zbl 0599.60044

[Sa] J. Sauvageot, Markov quantum semigroups admit covariant Markov C* dilations, Commun. Math. Phys., Vol. 106, 1986, pp. 91-103. | MR 853979 | Zbl 0606.60079

[St] W.F. Stinespring, Positive functions on C* algebras, Proc. Amer. Math. Soc., Vol. 6, 1955, pp. 211-16. | MR 69403 | Zbl 0064.36703

[Vi-S] G.F. Vincent-Smith, Dilations of a dissipative quantum dynamical system to a quantum Markov process, Proc. London Math. Soc. (3), Vol. 49, 1984, pp. 58-72. | MR 743370 | Zbl 0572.46055

[Y] K. Yosida, Functional Analysis, Springer Verlag, Berlin, 1965. | Zbl 0126.11504