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).
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Frigerio, A., Maassen, H. Quantum Poisson processes and dilations of dynamical semigroups. Probab. Th. Rel. Fields 83, 489–508 (1989). https://doi.org/10.1007/BF01845700
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DOI: https://doi.org/10.1007/BF01845700
Keywords
- Normal Weight
- Stochastic Process
- Probability Theory
- Markov Process
- Transition Operator