Quantum Poisson processes and dilations of dynamical semigroups
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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 algebraMn 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 semigroupetL of transition operators on (Mn, π) has generator whereu is an arbitrary unitary element of the centraliser of (Mn⊗ℳ,φ⊗μ).
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© Springer-Verlag 1989