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Quantum stochastic differential equations driven by free noises and dilations of Markovian semigroups. (English) Zbl 0803.60053

Quantum stochastic calculus with respect to free noises has been used to produce different dilations of Markovian semigroups with bounded generators. The aim of this paper is to extend these results to a bigger class of Markovian semigroups. For this end we establish an existence, uniqueness and unitary theorem for quantum stochastic differential equations with unbounded coefficients driven by infinite creation and annihilation and gauge fields. We show that, even if the free noise fields satisfy a different ItĂ´ table, it turns out that the unitary cocycles obtained as solutions of quantum stochastic differential equations driven by free noise fields, can be used to construct unitary dilations of the same class of quantum stochastic differential equations dilated by unitary cocycles in the boson Fock space.
Reviewer: M.E.Mancino (Povo)

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
81S25 Quantum stochastic calculus
60K40 Other physical applications of random processes
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