[Acc78] On the quantum Feynman-Kac formula. Rendiconti del Seminario Mathematico e Fisico di Milano, 48, pp. 135–180, 1978.
[AC82] Conditional expectation in von Neumann algebra and a theorem of Takesaki. J. Funct. Anal., 45, pp. 245–273, 1982.,
[AFH06] Generic q-Markov semigroups and speed of convergence of q-algorithms, Infinite Dim. Anal. Quant. Prob. and Related Topics, 9, pp. 567–594, 2006., ,
[AFL82] Quantum stochastic processes. Publ. Res. Inst. Math. Sci., 18, pp. 97–133, 1982., ,
[AFL90] The weak coupling limit as a quantum functional central limit. Comm. Math. Phys., 131, pp. 537–570, 1990., ,
[AK91] Quantum Markov chains: The recurrence problem. Quantum Probability and Related Topics, 7, 63–73, 1991.,
[AK02] QP-PQ Quantum Probability and White Noise Analysis, 14, World Scientific, Singapore, 14, 1–192, 2002., Lectures on quantum interacting particle systems, Quantum interacting particle systems (Trento, 2000).
[AL91] Squeezing noises as weak coupling limit of a Hamiltonian system. Rep. Math. Phys., 29, 227–256, 1991. and .
[ALV02] Berlin, 2002., , Quantum Theory and Its Stochastic Limit. Springer,
[AL87] Quantum Dynamical Semigroups and Applications. Lecture Notes in Physics, 286, Springer, Berlin, 1987.,
[Arv02] The heat flow of the CCR algebra. Bull. London Math. Soc., 34, 73–83, 2002.
[Att03] Quantum Noises. Lecture Notes of the Summer School on Quantum Open Systems. Grenoble, 2003.
[AC04] Quantum stopping times and quasi-left continuity. Ann. Inst. H. Poincaré Probab. Statist., 40, pp. 497–512, 2004.,
[AL04] Quantum stochastic calculus with maximal operator domains. Ann. Probability, 32, pp. 488–529, 2004.,
[AP96] 1996., Strong Markov processes and the Dirichlet problems on C*-algebras. Prepublications de l'Institute Fourier, Grenoble, 357,
[AS98] Stopping semimartingales on Fock space. Quantum Probability Com-munication, X, World Scientific, Singapore, 1998.,
[AyS87] Probability Theory and Applications, Proc. World Congr. Bernoulli Soc., Tashkent, USSR, 1, pp. 445–454, 1987., Markov operators on quantum probability sapce, in
[ADR69] Proprietes relatives des processus de Markov recurrents. Z. Wahr. and Verw. Gebiete, 13, pp. 286–314, 1969., ,
[Bar03] Continual Measurements in Quantum Mechanics and Quantum Stochastic Calculus. Ecole d'éte de Mathematiques Grenoble, 2003.
[BL86] Stopping noncommutative processes. Math. Proc. Camb. Phil. Soc., 99, pp. 151–161, 1986.,
[BDK10] On the long time behavior of free stochastic Schrödinger evolutions. Rev. Math. Phys., 22, pp. 55–89, 2010., ,
[BN11] The structure of state space concerning quantum dynamical semigroups. ar Xiv: 1101. 3914. v 1, 2011.,
[Bel89] A new wave equation for a continuous nondemolition measurement. Phys. Lett. A, 140, pp. 355–358, 1989.
[Bel92a] Quantum continual measurements and a posteriori collapse on CCR. Comm. Math. Physics, 146, 611–635, 1992.
[Bel92b] Quantum stochastic calculus and quantum nonlinear filtering. J. Multivariate Analysis, 42, 171–201, 1992.
[BNM09] Dynamical programming of continuously observed quantum systems. ar Xiv: 0805.474.2 [quant-ph], Jan. 26, 2009., ,
[BO02] Entanglement, quantum entropy, mutual information. R. Soc. Lond. Proc.Ser. A, 458, pp. 209–231, 2002.,
[BS89] A quantum particle undergoing continuous observation. Phys. Lett. A, 140, pp. 359–362, 1989.,
[Bel13] On stopping Fock-space processes. ar Xiv: 1311. 4871 v1 [math.OA], November 19, 2013.
[BLS12] Quantum Feymann-Kac perturbations. ar Xiv: 1202. 6489v1, 2012., ,
[BDSW96] Mixed state entanglement and quantum error correction. Phys. Rev. A, 54, pp. 3824–3851, 1996., , ,
[Bha93] Markov Dilation of Nonconservative Quantum Dynamical Semigroups and a Quantum Boundary Theory. Doctoral dissertation, Indian Statistical Institute, 1993..
[BP94] Kolmogorov's existence theorem for Markov processes in C*-algebras. Proc. Indian Academy of Sciences, 104, pp. 253–262, 1994.,
[BP95] Markov dilations of non-conservative dynamical semigrouops and a quantum boundary theory. Annales de l'Institut H. Poincaré, 31, pp. 601–652, 1995.,
[BS94] Examples of unbounded generators leading to nonconservative minimal semigroups. Quantum Probability and Related Topics, IX, pp. 89–104, 1994.,
[Bia96] Quelques proprietes du mouvement Brownien non-commutatif. Hommage à P.A. Meyer et J. Neveu. Asterisque, 236, pp. 73–102, 1996.
[Bil68] Convergence of Probability Measures. John Wiley and Sons, New York-London-Sydney-Toronto, 1968.
[BG68] Markov Processes and Potential Theory, Academic Press, New York, 1968., .
[Boc33] Integration von Funktionen, deren Werte die Elemente eines Vectorraumes sind. Fundamenta Mathematicae, 20, pp. 262–276, 1933.
[Bou04] Filtering and Control in Quantum Optics. Ph.D thesis, University of Nijmegen, 2004..
[BGM04] Stochastic Schrödinger equations. J. Phys. A, 37, pp. 3189–3209, 2004., ,
[BMK03] Constructing the Davis process ofresonance fluorescence with quantum stochastic calculus. Optics and Spectroscopy, 94, pp. 911–919, 2003., ,
[BvH06] Quantum filtering: A reference probability approach. arxiv:math-ph/0508006v4, 2006.,
[BvH06] On the separation principle of quantum control. arXiv, 2006.,
[BvH08] Discrete approximation of quantum stochastic models. ar Xiv:0803.4383, 2008.,
[BvHJ07] An introduction of quantum filtering. SIAMJ. Contr. Optim., 46, pp. 2199–2241, 2007., ,
[BvHJ06b] 2006., discrete invitation to quantum filtering and feedback control. Preprint,
[BvHS07] Approximation and limit theorems for quantum stochastic models with unbounded coefficients. arXiv: 0712.2276 [math-ph], 2007., ,
[BR87] Operator Algebras and Quantum Statistical Mechanics I. 2nd ed., Springer, Berlin, 1987.,
[Bre68] Probability. SIAM, Philadelphia, 1968.
[BP06] The Theory of Open Quantum Systems. Oxford University Press, Oxford, 2006.,
[Car00] Exponential Ergodicity of a Class of Quantum Markov Semigroups. Tesi di Dottorato. University di Milano, 2000.
[Cha08] Stochastic Control of Hereditary Systems and Applications. Series on Stochastic Modelling and Applied Probability 59, Springer, New York, 2008.
[Cha12] Discrete approximations of controlled stochastic systems with memory: A survey. Stochastic Analysis and Applications, 30, pp. 675–724, 2012.
[Cha14a] A survey on invariance and ergodicity of quantum Markov semigroups. Stochastic Analysis and Applications, 32, pp. 380–454, 2014.
[Cha14b] Recurrence and transience of quantum Markov semigroups. To appear in Probability Surveys.
[CPP08] Optimal control of stochastic functional differential equations with bounded memory. Stochastics, 80, pp. 69–96, 2008., ,
[CPY09] Optimal stopping problems for stochastic differential equations with random coefficients. SIAM J. Control & Optimization, 48, pp. 941–971, 2009., ,
[Che90a] The Theory of Conservative Dynamical Semigroups and Application. MIEM preprint no. 1, Moscow, March 1990.
[Che90b] Contemporay Problems of Mathematics, Newest Achievements, 36, pp. 149–184, VINITI, Moscow, 1990.Necessary and Sufficient Conditions of the conservativeness of dynamical semigroups. In
[Che91] Necessary and sufficient conditions of the conservativeness of dynamical semigroups. J. Sov. Math., 56, pp. 2697–2719, 1991.
[Che93] Sufficient conditions of the conservativism of a minimal dynamical semigroup, Math. Notes 52, pp. 1067–1077, 1993.
[CF98] Sufficient conditions for conservativity of minimal quantum dynamical semigroups. J. Funct. Anal., 153, pp. 382–404, 1998.,
[CF95] XXIX, pp. 1–16, Lecture Notes in Mathematics, 1613, Springer, Berlin, 1995., On quantum extensions of the Azema martingale semigroup. Sem. Prob.,
[Chi06] Brazil. Available at http://www.wisdom.weizmann.ac.il/pavel/, 2006.Stability of nonlinear filters. A survey. Mini-course lecture notes, Petropolis,
[CvH07] Model robustness of finite state nonlinear filtering over the infinite time horizon. Ann. Appl. Prob., 17, pp. 688–715, 2007.,
[Cho04] Quantum dynamic semigroup and its asymptotic behaviors. Bull. Korean Math. Soc., 41, pp. 189–198, 2004.
[CE79] Cohomology of operator algebras and quantum dynamical semigroups. J. London Math. Society, 20, pp. 358–368, 1979. and
[Chu60] Markov Chains with Stationary Transition Probability. Springer, Berlin, 1960.
[Com00] A Non-Commutative Topological Theory of Capacities and Applications. Ph.D thesis, Pontificia Universidad Catolica de Chile, Facultad de Mathematicas, 2000.
[Com03] Criteria for large deviations, Trans. Amer. Math. Soc., 355, pp. 2905–2923, 2003.
[Com05] Functional approach of large deviations in general spaces, J. Theoretical Prob., 18, pp. 187–207, 2005.
[Com06] Upper regularization for extended self-adjoint operators. J. Operator Theory, 55, pp. 91–116, 2006.
[Con94] A Course in Functional Analysis. 2nd ed. Springer, Berlin, 1994.
[Coq00] Why are there only three quantum noises., Probab. Theory Relat. Fields, 118, pp. 349–364, 2000.
[Coq06] The optional stopping theorem for quantum martingales. J. Funct. Anal., 238, pp. 149–180, 2006.
[DPZ92] Da Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge, 1992.,
[DL92] Mathematical Analysis and Numerical Methods for Science and Technology. 5, Evolution Problems I. Springer, Berlin, 1992.,
[Dav69] Quantum stochastic processes, Comm. Math. Physics, 15, pp. 277–304, 1969.
[Dav74] Markovian master equation. Commun. Math. Phys., 39, pp. 91–110, 1974.
[Dav76] Quantum Theory of Open Systems. Academic Press, London, New York, San Francisco, 1976.
[Dav77] Quantum dynamical semigroups and the neutron diffusion equation. Rep. Math. Phys., 11, pp. 169–188, 1977.
[Dav79] Generators of dynamical semigroups, J. Funct. Analysis, 34, pp. 421–432, 1979.
[Dav80] One-Parameter Semigroups. Academic Press, New York, 1980.
[DL70] An operational approach to quantum probability theory. Comm. Math. Physics, 17, pp. 239–260, 1970.
[DM87] Probabilites et potentiel. 2nd ed. Hermann, Paris, 1987.,
[Dir39] A new notation for quantum mechanics. Math. Proceedings of the Cambridge Phil. Society, 35, pp. 416–418, 1939.
[Dix69] Les C*-algebres et leurs representations. Gauthier Villars, Paris, 1969.
[Dix81] Von Neumann Algebras. North Holland, Amsterdam, 1981.
[DU77] Vector Measures. American Mathematical Society, Providence, RI, 1977.,
[Dio88] Continuous quantum measurement and Ito formalism. Phs. Lett. A, 129, pp. 419–423, 1988.
[DS63] Linear Operator: Parts I, II, & III. Interscience, John Wiley, New York, 1963.,
[Dyn65] Markov Processes, vols. 1 and 2. Mathematischen wissenschaften, Springer, Berlin-New York, 1965.
[EW03] Quantum Probability and Infinite Dimensional Analysis, Burg, 2001, QP-PQ: Quantum Probab. White Noise Anal., 15, pp. 78–83, World Scientific, Singapore, 2003., Aymptotic behavior of Markov semigroup on noncommutative L1-spaces. In
[EW06] Aymptotic behavior of Markov semigroup on preduals of von Neumann algebras. J. Math. Analy. Appl., 314, pp. 749–763, 2006.,
[Enc88] Bull. Unione Mat. Ital., 2, pp. 19–39, 1988. space valued quasimartingales.
[EK85] Markov Processes, Characterization and Convergence. Wiley Series in Probability and Statistics. John Wiley and Sons, New York, 1985. and
[Eva77] Irreducible quantum dynamical semigroups. Comm. Math. Phy., 54, pp. 293–297, 1977.
[EHO79] The generators of positive semigroups, J. Functional Analysis, 32, pp. 207–212, 1979.,
[EHK78] Spectral properties of positive maps on C*-algebras. J. London Math. Soc., 17, pp. 345–355, 1978.
[EL77] Dilations of irreducible evolutions in algebraic quantum theory. Commun. Dublin Inst. Adv. Studies, Ser A, 24, 1977.,
[Fag90] On quantum stochastic differential equations with unbounded coefficients. Probab. Th. Rel. Fields, 86, pp. 501–516, 1990.
[Fag91] Pure birth and pure death processes as quantum flows in Fock space. Sankhya, 53, pp. 288–297, 1991.
[Fag92] Unitarity of solutions of quantum stochastic stochastic differential equations and conservativity of the associated semigroups. Quantum Probability and Related Topics, VII, pp. 139–148, 1992.
[Fag93] Characterization of isometric and unitary weakly differentiable cocycles in Fock space. Quantum Probability and Related Topics, VIII, pp. 143–164, 1993.
[Fag99] Quantum Markov semigroups and quantum flows. Proyecciones, 18, pp. 1–144, 1999.
[Fag04] Quantum Markov semigroups: Structure and asymptotics. Rend. Circ. Palermo serie II Suppl., 2004.
[Fag06] Quantum stochastic differential equations and diltation of completely positive semigroups. Open Quantum Systems II, Lecture Notes in Mathematics, 1881, pp. 183–220, 2006.
[FM13] Stochastic Schrödinger equations and applications to Ehrenfest-type theorems. arXiv: 1207.2939v2 [quant-ph], March 19, 2013.,
[FR96] An ergodic theorem in quantum optics, pp. 73–86 in Proceedings of the Univ. of Udine Conference in Honour of A. Frigerio, Editrice Universitaria Udinese, 1996.,
[FR98] The approach to equilibrium of a class of quantum dynamical semigroups. Infinite Dimensional Analysis and Quantum Probability, 1, pp. 561–572, 1998.,
[FR00] Preprint, 2000., On the existence of invariant states for quantum dynamical semigroups.
[FR02a] Subharmonic projections for a quantum semigroup. J. Math. Phys., 43, pp. 1074–1082, 2002.,
[FR02b] Quantum Probability and White Noise Analysis, 14, World Scientific, Singapore, pp. 197–240, 2002., Lectures on the qualitative analysis of quantum Markov semigroups. In
[FR03] Transience andrecurrence of Quantum Markov semigroups. Probab.Theory Relat. Fields, 126, pp. 289–306, 2003.,
[FR03] Stochastic Analysis and Mathematical Physics II, Birkhauser, Berlin, 2003., Quantum Markov semigroups and their stationary states.
[FRS94] Quantum flows associated to master equations in quantum optics. J. Math. Phys., 35, pp. 1–12, 1994., ,
[FW00] Mild solutions of quantum stochastic differential equations. Electronic Communications in Probability, 5, pp. 158–171, 2000.
[FW03] Solving quantum stochastic differential equations with unbounded coefficients. J. Funtional Analy., 198, pp. 279–310, 2003.,
[Fel40] On the integro-differential equations for purely discontinuous Markov processes, Trans. AMS, 48, pp. 488–575, 1940.
[Fel50] An Introduction to Probability Theory and Its Applications. Vol. I. John Wiley & Sons, New York, 1950.
[Fri77] Quantum dynamical semigroups and approach to equilibrium. Lett. Math. Phys., 2, pp. 79–87, 1977.
[Fri78] Stationary states of quantum dynamical semigroups. Comm. Math. Phys., 63, pp. 269–276, 1978.
[FV82] Long time asymptotic properties of dynamical semigroups on w*-algebras. Math. Zeitschrift, 80, pp. 275–286, 1982.,
[GZ04] Quantum Noise. 3rd edn., Springer, Berlin, 2004.,
[GK12] A coherent approach to recurrence and transience for quantum Markov operators. arXiv: 1211.6876v1 [math.OA], November 29, 2012.,
[Get80] Seminaire de probabilites, XIV(Paris, 1978/1979), Lecture Notes in Mathematics. 784, Springer, Berlin, 1980, pp. 397–409.Transience and recurrence of Markov processes.
[GP92] The quantum-state diffusion model applied to open systems. J. Phys. A, 25, 5677, 1992.,
[Gou08] 2008.Optimal quantum feedback control for canonical observables. Preprint,
[GS04] Stochastic Schrödinger equations as limit of discrete filtering, Open Systems & Information Dynamics, 11, pp. 235–255, 2004.,
[Gle57] Measures on the closed subspaces of Hilbert spaces. J. Math. Mechanics, 6, pp. 885–893, 1957.
[GKS76] Completely positive dynamical semigroups of N-level systems. J. Math. Physics, 17, pp. 821–825, 1976., ,
[Gri05] Optimal Control of Quantum Systems. Ph.D. thesis, University of California, Santa Barbara, 2005.
[Gro86] One-Parameter Semigroups of Positive Operators, edited by . Lecture Notes in Mathematics 1184, Springer, Berlin, 1986.Asympototics of positive semigroups on C*- and W*-algebras. In
[Gron19] H.Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. of Math., 20, pp. 292–296, 1919.
[GVWW12] Recurrence for discrete time unitary evolutions. arXiv: 1202.3903 [quant-ph], 2012., , ,
[Gud79] Radon-Nikodym theorem for *-algebras. Pacific J. Math., 80, pp. 141–149, 1979.
[GS91] Regular quantum Markov processes. Math. Phys., 32, pp. 656–668, 1991.,
[Gui70] Symmetric Hilbert Spaces and Related Topics. Lecture Notes in Mathematics 261, Springer, Berlin, 1970.
[Gui74] Systémes dynamiques non commutatifs. Astérisque, 13–14, pp. 1–203, 1974.
[HS80] Odense University, 1980., Geometric aspects of the Tomika-Takesaki theory I & II, preprint No. 3, Mathematics Department,
[Has80] Stochastic Stability of Differential Equations. Sijthoff Noordhoff, Amsterdam, 1980.
[HG08] Guide to mathematical concepts of quantum theory. ACTA Physica Slovaca, 58, 487–674, August 2008.,
[HP57] Functional Analysis and Semigroups, 2nd ed., American Mathematical Society, Providence, RI, 1957.,
[Hol95] On the structure of covariant dynamical semigroups. J. Functional Analysis, 131, pp. 255–278, 1995.
[Hol01] Statistical Structure of Quantum Theory. Sprinter, Berlin, 2001.
[HS05] Continuous ensembles and the χ-capacity of infinite dimensional channels. Probab. Theory and Its Appl., 50, pp. 98–114, 2005.,
[HSW05] On the notion of entanglement in Hilbert space. Russian Math. Surveys, 60, pp. 153–154, 2005., ,
[Hud06] 2006.Stop times in Fock space quantum probability. Preprint,
[HP84] Quantum Itô's formula and stochastic evoluation. Comm. Math. Physics, 93, pp. 301–323, 1984.,
[IW81] Stochastic Differential Equations and Diffusion Processes. North-Holland Mathematical Library 24, North-Holland, Amsterdam-New York, 1981.,
[Kat95] Perturbation theory for linear operators. Corr. printing of the 2nd ed. Springer, New York, 1995.
[Kol50] Foundations of Probability Theory, Chelsea, New York, 1950.
[Kolo00] Semiclassical Analysis for Diffusion and Stochastic Processes. Lecture Notes in Mathematics 1724, Springer, Berlin, 2000.
[Kra70] General state charges in quantum theory. Ann. Phys., 64, pp. 311–335, 1970.
[Kra83] State, Effects, and Operations Fundamental Notions of Quantum Theory. Lecture Notes in Physics, 190, Springer, Berlin, 1987.
[Kre89] Introductory Functional Analysis with Applications. Wiley Classics Library Edition, John Wiley & Sons, New York, 1989.
[Kum02] Coherent Evolution in Noisy Environments, Lecture Notes in Physics 611, Springer, Berlin, 2002.Quantum Markov processes. In
[Kus67] Stochastic Stability and Control. Academic Press, Singapore, 1967.
[Lin76] On the generators of quantum dynamical semigroups. Comm. Math. Phys., 48, pp. 119–130, 1976.
[LSin10] A quantum stochastic Lie-Trotter product formula. Indian J. Pure Appl. Math., 40, pp. 313–325, 2010.,
[LS10] 2010., On quantum stochastic differential equations. Preprint.
[LW00] Existence, positivity and contractivity for quantum stochastic flows with infinite dimensional noise. Probab. Theory Related Fields, 116, pp. 505–543, 2000.,
[LW10] Quantum stochastic cocycles and completely bounded semigroups on operator spaces. arXiv:1101.0177v1, 2010.,
[Liu12] Derivation of quantum walk equalities using quantum Feymann-Kac formula. arXiv: 1201.1557v3, 2012.
[Luc95] Ergodic projection for quantum dynamical semigroups. International J. Theor. Phys., 34, 1995.
[LP61] Dissipative operators in a Banach space. Pacific J. Math, 11, pp. 679–698, 1961.,
[Maa03] Quantum Probability Theory. Lecture Notes, Radboud University, Nijmegen, 2003.
[Mao97] Stochastic Differential Equations and Applications. Horwood Publishing, Chichester, 1997.
[Mer98] Quantum Mechanics. 3rd edition. Wiley, New York, 1998.
[Mey95] Quantum Probability for Probabilists, 2nd ed., Lecture Notes in Mathematics 1538, Springer, Berlin, Heidelberg, New York, 1995.
[MvH07] Stabilizing feedback controls for quantum systems. SIAM J. Control & Optimization, 46, pp. 445–467, 2007.,
[Moh91] Quantum stochastic differential equations with unbounded coefficients and dilations of Feller's minimal solution. Sankhya Ser. A, 53, pp. 255–287, 1991.
[Moh05] A resolution of quantum dynamical semigroups. arXiv:math/0505384, 2005.
[Mor04] Numerical simulation of stochastic evoluation equations associated to quantum Markov semigroups. Math. Comp., 247, pp. 1393–1415, 2004.
[Mor05] Numerical solution of conservative finite-dimensional stochastic Schrödinger equations. Ann. Appl. Probab., 15, pp. 2144–2171, 2005.
[Mor08] Heisenberg evolution of quantum observables represented by unbounded operators. J. Funct. Anal., 255, pp. 3249–3273, 2008.
[Mor13] Regularity of solutions to quantum master equations: A stochastic approach. To appear in Ann. Probab., 41, pp. 1978–2012, 2013.
[MR07] 2007., Nonlinear Schrodinger equations. Preprint.
[MR06] Basic properties of nonlinear Schrödinger equations driven by Brownian motions. Annals Appl. Prob., 18, pp. 591–619, 2008.,
[Nag90] Real Analysis. Lecture notes, Kansas State University, Manhattan, KS, 1990.
[Ngo74] Classification des systémes dynamiques noncommutatifs. J. Functional Analysis, 15, pp. 188–201, 1974.
[NC00] Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2000.,
[Nie83] Absolute continuity for linear forms on B*-algebras and a Radon-Nikodym type theorem (quadratic version). Rend. Circ. Mat. Palermo (2), 32, pp. 358–376, 1983.
[NKI08] Effects of time delay in feedback control of linear quantum systems. arXiv:0811.460.1 [quant-ph], November 27, 2008., ,
[Oba97] Quantum stochastic differential equations in terms of quantum white noise. Nonlinear Analysis, Theory, Methods & Applications, 30, pp. 279–290, 1997.
[Oks98] Stochastic Differential Equations. 5th ed. Springer, Berlin, 1998.
[Ond04] Uniqueness for stochastic evolution equations in Banach spaces. Dissertationes Mathematicae, 426, 2004.
[Oza85] Concepts of conditional expectations in quantum theory. J. Math. Physics, 26, pp. 1948–1955, 1985.
[Par67] Probability Measures on Metric Spaces. Academic Press, New York and London, 1967.
[Par92] An Introduction to Quantum Stochastic Calculus. Monographs in Mathematics 85, Birkhauser, Basel-Boston-Berlin, 1992.
[PS87] Stop times in Fock space stochastic calculus. Probab. Th. Rel. Fields, 75, pp. 317–349, 1987.,
[Paz83] Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York, 1983.
[Pel08] Existence, uniqueness and approximation of a stochastic Schrodinger equation: The diffusion case. Ann. Probab., 36, pp. 2332–2353, 2008.
[Pel09] Existence, uniqueness and approximation of a stochastic Schrödinger equation: The Poisson case. arXiv:0709.3713v2[math.PR], March, 6, 2009.
[Per98] Quantum State Diffusion. Cambridge University Press, Cambridge, 1998.
[Per83] Scattering Theory by the Enss Method. Harwood Academic, Reading, UK, 1983.
[Pro04] Stochastic Integration and Differential Equations. 2nd ed. Springer, Berlin 2004.
[Reb92] Second Symposium on Probability Theory and Stochastic Processes, First Mexican-Chilean Meeting on Stochastic Analysis (Guanajuato, 1992), Soc. Mat. Mexicana, Mexico City.Entropy functionals in quantum probability. In
[Reb97] On the recurrence of Quantum Dynamical Semigroups. Proc. ANESTOC'96, World Scientific, pp. 130–141, 1997.
[RS70] Methods of Modern Mathematical Physics I. Academic Press, San Diego, 1970.,
[RS75] Methods of Modern Mathematical Physics II. Academic Press, San Diego, 1975.,
[Rev75] Markov Chains. North-Holland Publishing Co., Amsterdam, 1975.
[RY99] Continuous Martingales and Brownian Motion. 3rd ed. Springer, Berlin, 1999.,
[RH11] Introduction to the time evoluation of open quantum systems. arXiv:1104.5242v1 [quant-ph], April 27, 2011.,
[Rud87] Real and Complex Analysis. McGraw Hill, New York, 1987.
[Rud91] Functional Analysis. 2nd ed. McGraw-Hill Science/Engineering/Mathematics, New York, 1991.
[Sak98] C*-algebras and W*-algebras. Classics in Mathematics, Springer, Berlin, 1998.
[SSF04] Another dual formulation of the separability problem. Phys.Rev. A, 70, 054102, 2004., ,
[SG87] The regularity of monotone continuous compressions on von Neumann algebras. Dokl. AN Uz. SSR, 6, pp. 9–11, 1987., .
[SL09] Vanishing quantum discord is necessary and sufficient for completely positive maps. Phys. Rev. Lett. 102, 100402, 2009.
[Sch05] Measures, Integrals and Martingales. Cambridge University Press, Cambridge, 2005.
[SM01] Quantum nonlinear dynamics of continuously measured systems. Phys. Rev. A, 63, 42101, 2001.,
[SJ08] Locally optimal control of quantum systems with strong feedback. arXiv:0803.270.2 [quant-ph], December 7, 2008.,
[SM10] 2010., Quantum stochastic stability. Preprint,
[Shi10a] Continuity of the von Neumann entropy. Commun. Math. Phys., 296, pp. 625–654, 2010.
[Shi10b] On properties of the space of quantum states and their application to construction of entanglement monotones. Izvestiya: Mathematics, 74, pp. 849–882, 2010.
[Shi11] Properties of probability measures on the set of quantum states and their applications. arXiv:math-ph/0607019v3, March 24, 2011.
[Sho97] Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. Mathematical Surveys and Monographs 49, American Mathematical Society, Providence, RI, 1997.
[SG07] Quantum Stochastic Processes and Noncommutative Geometry. Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 2007.,
[SP09] 2009 American Control Conference, Hyatt Regency Riverfront, June 10–12, St. Louis, MO, pp. 719–724, 2009., Lyapunov stability for quantum Markov processes.
[Spi94] Calculus. Cambridge University Press, Cambridge, 1994.
[SB01] Dynamics of open quantum systems initially entangled with environments beyond the Kraus representation. Phys. Rev. A 64, 062106, 2001.,
[Sti55] Positive functions on C*-algebras. Proc. Am. Math. Soc., 6, pp. 211–216, 1955.
[Sto32] On one-parameter unitary groups in Hilbert space. Annals of Math., 33, pp. 643–648, 1932.
[SV79] Multidimensional Diffusion Processes, Springer, Berlin, 1979., .
[Tak71] Conditional expectations in von Neumann algebras. J. Funct. Anal., pp. 306321, 1971.
[Tak79] Theory of Operator Algebras I. Encyclopaedia of Mathematical Sciences, 124, Springer, Berlin, 1979.
[Tho90] The Hahn-Banach Separation Theorem. Aarhus University, Advanced Analysis Lecture Notes, 1990.
[Tom57] On the projections of norm one in W*-algebra. Proc. Japan Acad., 33, pp. 608–612, 1957.
[TKOCM04] Operator-sum representation of time-dependent density operators and its applications. Phys. Rev. A, 69, 054102, 2004., , , ,
[Tro58] F. Approximation of semi-groups of operators. Pacific J. Math., 8, pp. 887–919, 1958.
[UMa05] Classification and Decomposition of Quantum Markov Semigroups. Doctoral Dissertation, Universita di Genova, 2005.
[UMa06] Classification and decomposition of quantum Markov semigroups. Probab. Theory Relat. Fields, 134, pp. 603–623, 2006.
[Ume54] Conditional expectation in an operator algebra. Thoku Math. J., 6, pp. 177–181, 1954.
[Ume56] Conditional expectation in an operator algebra, II. Thoku Math. J., 8, pp. 86–100, 1956.
[Ume59] Conditional expectation in an operator algebra, III.Kdai Math.Sem.Rep., 11, pp. 51–64, 1959.
[vHan07] Filtering, Stability, and Robustness. Ph.D. thesis, California Institute of Technology, 2007.
[vHan07] Observability and nonlinear filtering. Preprint, arXiv:0708.3412, 2007.
[vHan09a] 2009. Randonmization in C* -algebras and the stability of quantum filters. Preprint,
[vHan09b] Infinite Dimensional Analysis, Quantum Probability and Related Topics, 14, pp. 153–172, World Scientific, Singapore, 2008.The stability of quantum Markov filters. In
[vNeu55] Mathematical Foundations of Quantum Mechanics, translated by . Princeton University Press, Princeton, 1955.
[WS09] G. Analysis of Lyapunov method for control of quantum states: Non-generic case. arXiv:0901.4522v. [quant-ph], January 28, 2009.,
[Wat79] Ergodic theorems for W*-dynamical semigroups. Hokkaido Math. J., 8, pp. 176–190, 1979.
[Wis96] M. Quantum trajectories and quantum measurement theory. Quantum Semiclass. Opt., 8, pp. 205–222, 1996.
[Yea83] J. Measures on projections in W*-algebras of type II. Bull. London Math. Soc., 15, pp. 139–145, 1983.
[Yos80] Functional Analysis. Springer, Berlin, 1980.
[Zie90] Nonlinear Functional Analysis and Its Applications II. Linear Monotone Operators. Springer, New York, 1990.
[Zor35] A remark on method in transfinite algebra. Bulletin of the Amer. Math. Society, 41, pp. 667–670, 1935.