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Displaying similar documents to “Realisation of a class of Markov processes through unitary evolutions in Fock space”

Stationary Quantum Markov processes as solutions of stochastic differential equations

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,...

Markov chains approximation of jump–diffusion stochastic master equations

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...