Dilations à la Hudson–Parthasarathy of Markov Semigroups in Classical Probability

DOI10.1080/07362990802286475zbMath1157.60073arXivmath/0702784OpenAlexW1973303628MaRDI QIDQ3535733

Matteo Gregoratti

Publication date: 14 November 2008

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702784

zbMATH Keywords

Markov chainsdilationquantum dynamical semigroupquantum probabilityunitary dilationclassical Markov semigroup

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Noncommutative probability and statistics (46L53) Quantum stochastic calculus (81S25) Continuous-time Markov processes on discrete state spaces (60J27)

Cites Work

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• Palm probabilities and stationary queues
• Quantum Ito's formula and stochastic evolutions
• Covariant Markov dilations of quantum dynamical semigroups
• Within and beyond the reach of Brownian innovation
• The quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation
• Quantum Stochastic Differential Equation is Unitarily Equivalent to a Symmetric Boundary Value Problem in Fock Space
• ON THE HAMILTONIAN OPERATOR ASSOCIATED TO SOME QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS
• The Hamiltonian operator associated with some quantum stochastic evolutions

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