Displaying similar documents to “On the existence of a class of stationary quantum stochastic processes”

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,...

Quantum stochastic processes arising from the strong resolvent limits of the Schrödinger evolution in Fock space

Alexander Chebotarev, Dmitry Victorov (1998)

Banach Center Publications

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By using F. A. Berezin's canonical transformation method [5], we derive a nonadapted quantum stochastic differential equation (QSDE) as an equation for the strong limit of the family of unitary groups satisfying the Schrödinger equation with singularly degenerating Hamiltonians in Fock space. Stochastic differentials of QSDE generate a nonadapted associative Ito multiplication table, and the coefficients of these differentials satisfy the formal unitarity conditions of the Hudson-Parthasarathy...