Realisation of a class of Markov processes through unitary evolutions in Fock space
Kalyanapuram Rangachari Parthasarathy (1991)
Séminaire de probabilités de Strasbourg
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Kalyanapuram Rangachari Parthasarathy (1991)
Séminaire de probabilités de Strasbourg
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Jürgen Hellmich, Claus Köstler, Burkhard Kümmerer (1998)
Banach Center Publications
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From the operator algebraic approach to stationary (quantum) Markov processes there has emerged an axiomatic definition of quantum white noise. The role of Brownian motion is played by an additive cocycle with respect to its time evolution. In this report we describe some recent work, showing that this general structure already allows a rich theory of stochastic integration and stochastic differential equations. In particular, if a quantum Markov process is represented by a unitary cocycle,...
Clément Pellegrini (2010)
Annales de l'I.H.P. Probabilités et statistiques
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are solutions of stochastic differential equations obtained when describing the random phenomena associated to quantum continuous measurement of open quantum system. These equations, also called or , are usually of two different types: diffusive and of Poisson-type. In this article, we consider more advanced models in which jump–diffusion equations appear. These equations are obtained as a continuous time limit of martingale problems associated to classical Markov chains...
Adam Majewski, Robert Olkiewicz, Bogusław Zegarliński (1998)
Banach Center Publications
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We show that recently introduced noncommutative -spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.
J. Martin Lindsay, Adam G. Skalski (2005)
Annales de l'I.H.P. Probabilités et statistiques
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John Gough (2006)
Banach Center Publications
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We present quantum stochastic calculus in terms of diagrams taking weights in the algebra of observables of some quantum system. In particular, we note the absence of non-time-consecutive Goldstone diagrams. We review recent results in Markovian limits in these terms.
Robin Hudson, Martin Lindsay (1985)
Annales de l'I.H.P. Physique théorique
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Maria Elvira Mancino (1994)
Rendiconti del Seminario Matematico della Università di Padova
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