Quantum Ito's formula and stochastic evolutions View Full Text


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Article Info

DATE

1984-09

AUTHORS

R. L. Hudson, K. R. Parthasarathy

ABSTRACT

Using only the Boson canonical commutation relations and the Riemann-Lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes. This leads to a noncommutative Ito product formula, a realisation of the classical Poisson process in Fock space which gives a noncommutative central limit theorem, the construction of solutions of certain noncommutative stochastic differential equations, and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps. The classical Ito product formula for stochastic differentials with respect to Brownian motion and the Poisson process is a special case. More... »

PAGES

301-323

References to SciGraph publications

  • 1983. Towards a theory of noncommutative semimartingales adapted to Brownian motion and a quantum Ito's formula in THEORY AND APPLICATION OF RANDOM FIELDS
  • 1977. Statistics of Random Processes I, General Theory in NONE
  • 1978-12. On the quantum Feynman-Kac formula in RENDICONTI DEL SEMINARIO MATEMATICO E FISICO DI MILANO
  • 1976-06. On the generators of quantum dynamical semigroups in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1984. Construction of quantum diffusions in QUANTUM PROBABILITY AND APPLICATIONS TO THE QUANTUM THEORY OF IRREVERSIBLE PROCESSES
  • 1982-02. Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1984. Stochastic Dilations of Uniformly Continuous Completely Positive Semigroups in POSITIVE SEMIGROUPS OF OPERATORS, AND APPLICATIONS
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    http://scigraph.springernature.com/pub.10.1007/bf01258530

    DOI

    http://dx.doi.org/10.1007/bf01258530

    DIMENSIONS

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