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Contents of PMS, Vol. 21, Fasc. 1,
pages 231 - 251
 

ON q -DEFORMED QUANTUM STOCHASTIC CALCULUS

Piotr Śniady

Abstract: In this paper we investigate a quantum stochastic calculus built 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 [8]. We define stochastic integrals and estimate them in the operator norm. We prove Itô’s formula as well.

1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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