Markov structure of quantum Lévy processes
Identifieur interne : 002359 ( Istex/Checkpoint ); précédent : 002358; suivant : 002360Markov structure of quantum Lévy processes
Auteurs : Uwe Franz [Allemagne] ; René Schott [France]Source :
- Mathematics and Its Applications
Abstract
Abstract: In this chapter we will consider the question which quantum stochastic processes admit classical versions, i.e. for what families of operators (Xt)t∈I there exists a classical stochastic process (X͂t)t∈I on some probability space (Ω, F, P) such that all time-ordered moments agree, i.e. (5.1) $$\Phi (X_{{t_1}}^{{k_1}} \cdots X_{{t_n}}^{{k_n}}) = IE(\tilde X_{{t_1}}^{{k_1}} \cdots \tilde X_{tn}^{{k_n}}) $$ for all n, k 1,..., k n ∈ IN, t 1 ≤ ... ≤ t n ≤ I, for the (vacuum) state Φ.
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DOI: 10.1007/978-94-015-9277-2_5
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