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On q-deformed quantum stochastic calculus

Sniady P.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 1

231--251

In this paper we investigate a quantum stochastic calculus built of creation, annihilation and number of particles operators which fulfill some deformed com-mutation relations. Namely, we introduce a deformation of a number of particles operator which hassimple commutation relations with well-known q-deformed creation and annihilation operators. Since all operators considered in this theory are bounded, we do not dealwith some difficulties of a non-deformed theory of Hudson and Parthasarathy [8]. We define stochastic integrals and estimate them in the operator norm. We prove Itô’s formula as well.