Probability Theory and Related Fields

, Volume 83, Issue 4, pp 489–508 | Cite as

Quantum Poisson processes and dilations of dynamical semigroups

  • Alberto Frigerio
  • Hans Maassen
Article

Summary

The notion of a quantum Poisson process over a quantum measure space is introduced. This process is used to construct new quantum Markov processes on the matrix algebraM n with stationary faithful state π. If (ℳ, μ) is the quantum measure space in question (ℳ a von Neumann algebra and μ a faithful normal weight), then the semigroupe tL of transition operators on (M n , π) has generator
whereu is an arbitrary unitary element of the centraliser of (M n ⊗ℳ,φ⊗μ).

Keywords

Normal Weight Stochastic Process Probability Theory Markov Process Transition Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Alberto Frigerio
    • 1
  • Hans Maassen
    • 2
  1. 1.Dipartimento di Matematica e InformaticaUniversita di UdineUdineItaly
  2. 2.Mathematisch InstituutKatholieke Universiteit NijmegenNijmegenThe Netherlands

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