Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory
B. V. Rajarama Bhat; K. R. Parthasarathy
Annales de l'I.H.P. Probabilités et statistiques (1995)
- Volume: 31, Issue: 4, page 601-651
- ISSN: 0246-0203
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topRajarama Bhat, B. V., and Parthasarathy, K. R.. "Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory." Annales de l'I.H.P. Probabilités et statistiques 31.4 (1995): 601-651. <http://eudml.org/doc/77522>.
@article{RajaramaBhat1995,
author = {Rajarama Bhat, B. V., Parthasarathy, K. R.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {weak Markov flow; exit and entrance cocycles; exit time; boson Fock space; boundary theory for quantum Markov processes; nonconservative one parameter semigroups of completely positive linear contractions on a von Neumann algebra},
language = {eng},
number = {4},
pages = {601-651},
publisher = {Gauthier-Villars},
title = {Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory},
url = {http://eudml.org/doc/77522},
volume = {31},
year = {1995},
}
TY - JOUR
AU - Rajarama Bhat, B. V.
AU - Parthasarathy, K. R.
TI - Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1995
PB - Gauthier-Villars
VL - 31
IS - 4
SP - 601
EP - 651
LA - eng
KW - weak Markov flow; exit and entrance cocycles; exit time; boson Fock space; boundary theory for quantum Markov processes; nonconservative one parameter semigroups of completely positive linear contractions on a von Neumann algebra
UR - http://eudml.org/doc/77522
ER -
References
top- [AFL] L. Accardi, A. Frigerio and J.T. Lewis, Quantum stochastic processes, Proc. Res. Inst. Math. Sci., Kyoto, Vol. 18, 1982, pp. 97-133. Zbl0498.60099MR660823
- [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. Zbl0796.60092MR1280073
- [C1] K.L. Chung, Markov Chains with Stationary Transition Probabilities, Springer, Berlin, Gottingen. Heidelberg, 1960. Zbl0092.34304MR116388
- [C2] K.L. Chung, Lectures on the Boundary Theory for Markov Chains, Princeton University Press, 1970. Zbl0204.51003MR267644
- [CW] K.L. Chung and R.J. Williams, Introduction to Stochastic Integration, Birkhäuser, Boston. Basil. Stuttgart, 1983. Zbl0527.60058MR711774
- [Da] E.B. Davies, Quantum dynamical semigroups and the neutron diffusion equation, Rep. Math. Phys., Vol. 11, 1977, pp. 169-189. Zbl0372.47020MR503331
- [Dy] E.B. Dynkin, Markov Processes, Vol. I and II, Springer-Verlag, Berlin. Gottingen. Heidelberg, 1965. Zbl0132.37901MR193671
- [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. Zbl0365.46059
- [Em] G.G. Emch, Minimal dilations of CP flows, C* algebras and applications to physics, Springer LNM 650, 1978, pp. 156-159. Zbl0385.46035MR504761
- [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). Zbl0789.47027MR1186660
- [Fe1] W. Feller, Boundaries induced by non-negative matrices, Trans. of the Amer. Math. Soc., Vol. 83, No. 1, 1956, pp. 19-54. Zbl0071.34901MR90927
- [Fe2] W. Feller, On boundaries and lateral conditions for the Kolmogorov differential equations, Annals of Mathematics, Vol. 65, No. 3, 1957, pp. 527-70. Zbl0084.35503MR90928
- [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. Zbl0084.35503MR106508
- [H] R.L. Hudson, The strong Markov property for canonical Wiener processes, J. Func. Anal., Vol. 34, 1979, pp. 266-281. Zbl0424.46048MR552705
- [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. Zbl0485.46038MR649162
- [Me] P.A. Meyer, Quantum Probability for Probabilists, LNM 1538, Springer Verlag, 1993. Zbl0773.60098MR1222649
- [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. Zbl0751.60046
- [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. Zbl0743.46060
- [PS] K.R. Parthasarathy and K.B. Sinha, Stoptimes in Fock space stochastic calculus, Probab. Th. Rel. Fields, Vol. 75, 1987, pp. 317-349. Zbl0599.60044MR890283
- [Sa] J. Sauvageot, Markov quantum semigroups admit covariant Markov C* dilations, Commun. Math. Phys., Vol. 106, 1986, pp. 91-103. Zbl0606.60079MR853979
- [St] W.F. Stinespring, Positive functions on C* algebras, Proc. Amer. Math. Soc., Vol. 6, 1955, pp. 211-16. Zbl0064.36703MR69403
- [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. Zbl0572.46055MR743370
- [Y] K. Yosida, Functional Analysis, Springer Verlag, Berlin, 1965. Zbl0126.11504
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