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The interplay of classical and quantum stochastics: Diffusion, measurement and filtering

  • V. P. Belavkin
Part I: Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 457)

Abstract

A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative stochastic analysis and integration are outlined.

Algebraic differential equations that unify the quantum non Markovian diffusion with continuous non demolition observation are derived. A stochastic equation of quantum diffusion filtering generalising the classical Markov filtering equation to the quantum flows over arbitrary *-algebra is obtained.

Key words and phrases

quantum probability and noise noncommutative stochastic calculus quantum diffusion and flows continuous nondemolition processes a posteriori state diffusion and spontaneous localisation 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • V. P. Belavkin
    • 1
  1. 1.Mathematics DepartmentUK

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