On q-deformed quantum stochastic calculus

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.