2000/07/26 by Piotr Sniady
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.PR #math.QA #msc:81S25 #msc:05A30
published as Probab. Math. Statist. 21 (2001), no. 1, 231-251 · 18 pages
arxiv created 2000/07/26 · arxiv updated 2009/11/30
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.