  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. We define stochastic integrals and estimate them in
the operator norm. We prove Ito's formula as well.
