On Q-deformed Quantum Stochastic Calculus

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