Progrès récents en calcul stochastique quantique
Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 761, 13 p. 
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Meyer, Paul-André. Progrès récents en calcul stochastique quantique, dans Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 761, 13 p. http://archive.numdam.org/item/SB_1992-1993__35__35_0/

* Accardi (L.), Frigerio (A.) and Lewis (J.). Quantum stochastic processes, Publ. RIMS Kyoto, 18, 1982, p. 94-133. | MR | Zbl

* Accardi (L.), Journé (J. L.) et Lindsay (J. M.). On multidimensional markovian cocycles, QP.IV, p. 59-66.

Applebaum (D.). 1. Quantum stochastic parallel transport on non-commutative vector bundles, QP.III, p. 20-36. 2. Unitary evolutions and horizontal lifts in quantum stochastic calculus, Comm. Math. Phys., 140, 1991, p. 63-80. 3. Towards a quantum theory of classical diffusions on Riemannian manifolds, QP. VI, p. 93-111. | MR

* Barnett (C.), Streater (R. F.) et Wilde (I. F.). 1. The Ito-Clifford integral I, J. Funct. Anal. 48, 1982, p. 172-212. 2. - II, J. London Math. Soc. 27, 1983, p. 373-384. 3. - III, Markov properties of solutions to s.d.e.'s, Comm. Math. Phys. 89, 1983, p. 13-17. 4 -IV, a Radon-Nikodym theorem and bracket processes, J. Oper. Th. 11, 1984, p. 255-271. Belavkin (V. P.). A quantum non adapted Ito formula and stochastic analysis in Fock scale, J. Funct. Anal., 102, 1991, p. 414-447. | MR

Chebotarev (A. M.). The theory of conservative dynamical semigroups and its applications, à paraître. | Zbl

Chebotarev (A. M.) et Fagnola (F.). Sufficient conditions for conservativity of quantum dynamical semigroups. J. Funct. Anal., à paraître. | MR | Zbl

Davies (E. B.). Quantum Theory of Open Systems, Academic Press, 1976. | MR | Zbl

Evans (M.). Existence of quantum diffusions, Prob. Th. Rel. Fields, 81, 1989, p. 473-483. | MR | Zbl

Evans (M.) et Hudson (R. L.). * 1. Multidimensional quantum diffusions, QP.III, p. 69-88. 2. Perturbation of quantum diffusions, J. London Math. Soc., 41, 1992, p. 373-384. | MR | Zbl

Fagnola (F.). 1. On quantum stochastic differential equations with unbounded coefficients, Prob. Theory Rel. Fields, 86, 1990, p.501-516. | MR | Zbl

2. Pure birth and death processes as quantum flows in Fock space, Sankhya, ser. A, 53, 1991, p. 288-297. | MR | Zbl

3. Unitarity of solutions to quantum stochastic differential equations and conservativity of the associated quantum dynamical semigroup, QP. VII, à paraître. | Zbl

4. Chebotarev's sufficient conditions for conservativity of quantum dynamical semigroups, à paraître.

5. Diffusion processes in Fock space, à paraître.

6. Characterization of isometric and unitary weakly differentiable cocycles in Fock space, à paraître QP. VIII.

Fagnola (F.) et Sinha (K. B.). Quantum flows with unbounded structure maps and finite degrees of freedom, J. London M. Soc., à paraître. | MR | Zbl

* Gorini (V.), Kossakowski (A.) et Sudarshan (E.). Completely positive dynamical semigroups of n-level systems, J. Math. Phys., 17, 1976, p. 821-825. | MR

* Hudson (R. L.), Karandikar (R. L.) et Parthasarathy (K. R.). Towards a theory of non commutative semimartingales adapted to brownian motion and a quantum Ito's formula, Theory and Applications of Random Fields, Bangalore 1982, LNCI 49, 1983, p. 96-110. Hudson (R. L.) et Parthasarathy (K. R.). * 1. Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys., 93, 1984, p. 301-303. * 2. Stochastic dilations of uniformly continuous completely positive semigroups, Acta Appl. Math., 2, 1988, p. 353-398. * 3. Unification of fermion and boson stochastic calculus, Comm. Math. Phys., 104, 1986, p. 457-470. Hudson (R. L.) et Robinson (P.). Quantum diffusions and the noncommutative torus, Lett. Math. Phys., 15, 1988, p. 47-53. | MR

* Journé (J. L.). Structure des cocycles markoviens sur l'espace de Fock. Prob. Theory Rel. Fields, 75, 1987, p. 291-316. | MR | Zbl

* Lindblad (G.). On the generators of quantum dynamical semigroups. Comm. Math. Phys., 48, 1976, p. 119-130. | MR | Zbl

Meyer (P. A.). Quantum Probability for probabilists, à paraître aux LNM, 1993. | MR | Zbl

Mohari (A.). 1. Quantum stochastic calculus with infinite degrees of freedom and its applications. PhD thesis, ISI Delhi 1992. 2. Quantum stochastic differential equations with unbounded coefficients and dilations of Feller's minimal solution. Sankhya, ser. A, 53, 1991, p. 255-287. | MR | Zbl

Mohari (A.) et Parthasarathy (K. R.). 1. On a class of generalized Evans-Hudson flows related to classical Markov processes. 2. A quantum probabilistic analogue of Feller's condition for the existence of unitary Markovian cocycles in Fock space, preprint. | MR

Mohari (A.) et Sinha (K. B.). 1. Quantum stochastic flows with infinite degrees of freedom and countable state Markov processes. Sankhya, ser. A, 52, 1990, p. 43-57. | MR | Zbl

Parthasarathy (K. R.). 1. An Introduction to Quantum Stochastic Calculus, Birkhäuser, Basel 1992. | MR | Zbl

Parthasarathy (K. R.) et Sinha (K. B.). Boson-Fermion transformations in several dimensions, Pramana J. Phys., 27, 1986, p. 105-116. 2. Markov chains as Evans-Hudson diffusions in Fock space. Sém. Prob. XXIV, LNM 1426, 1990, p. 362-369. 3. Unification of quantum noise processes in Fock space, QP. VI, p. 371-384. | Numdam | MR | Zbl

VINcent-Smith (G. F.). 1. Unitary quantum stochastic evolutions, Proc. London Math. Soc., 63, 1991, p. 1-25 2. Quantum stochastic evolutions with unbounded generators, QP. VI, p. 465-472. | MR | Zbl