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Application of quasi-classical methods in a study of the Belavkin quantum filtration

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Literature cited

  1. 1.

    V. P. Belavkin, “A new wave equation for a continuous nondemolition measurement,” Phys. Lett. A.,140, 355–358 (1989).

  2. 2.

    V. P. Belavkin, “A reconstruction theorem for a quantum stochastic process,” Teor. Mat. Fiz.,62, No. 2, 409–431 (1985).

  3. 3.

    R. L. Hudson and K. R. Partasarathy, “Quantum Itô's formula and stochastic evolution,” Comm. Math. Phys.,93, 301–323 (1984).

  4. 4.

    A. S. Kholevo, “Quantum stochastic calculus,” in: Progress in Science and Technology. Contemporary Problems in Mathematics [in Russian], VINITI, Akad. Nauk SSSR,36, 3–28 (1989).

  5. 5.

    A. V. Skorokhod, “Operator stochastic differentiable equations and stochastic semigroups,” Usp. Mat. Nauk,37, 157–183 (1982).

  6. 6.

    V. P. Maslov, Perturbation Theory and Asymptotic Methods, Moscow State Unviersity, Moscow (1967).

  7. 7.

    V. P. Maslov, Operational Methods, Mir, Moscow (1974).

  8. 8.

    V. P. Maslov, “Global exponential asymptotics of solutions of tunnel equations and large deviation problems,” Tr. Mat. Inst. Steklov, Akad. Nauk SSSR,163, 150–180 (1984).

  9. 9.

    S. Yu. Dobrokhotov, V. N. Kolokol'tsov and V. P. Maslov, “Splitting of lower energetic levels of the Schrödinger equation and the asymptotics of the fundamental solution of the equation h (∂u/∂t)=(h2Δ/2−V (x)) u, ” Teor. Mat. Fiz.,87, No. 3, 323–375 (1991).

  10. 10.

    V. P. Belavkin and V. N. Kolokol'tsov, “A quasi-classical asymptotic of quantum stochastic equations,” Teor. Mat. Fiz.,89, No. 2 (1991).

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Translated from Matematicheskie Zametki, Vol. 50, No. 5, pp. 153–156, November, 1991.

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Kolokol'tsov, V.N. Application of quasi-classical methods in a study of the Belavkin quantum filtration. Mathematical Notes of the Academy of Sciences of the USSR 50, 1204–1206 (1991). https://doi.org/10.1007/BF01157713

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Keywords

  • Filtration
  • Quantum Filtration