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ON EXISTENCE OF SOLUTION FOR IMPULSIVE PERTURBED QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS AND THE ASSOCIATED KURZWEIL EQUATIONS

Journal: IMPACT : International Journal of Research in Applied, Natural and Social Sciences ( IMPACT : IJRANSS ) (Vol.2, No. 1)

Publication Date:

Authors : ; ;

Page : 51-60

Keywords : Impulsive; Kurzweil Equations; Bounded Variation; Noncommutative Stochastic Processes;

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Abstract

Existence of solution of impulsive Lipschitzian quantum stochastic differential equations (QSDEs) associated with the Kurzweil equations are introduced and studied. This is accomplished within the framework of the Hudson-Parthasarathy formulation of quantum stochastic calculus and the associated Kurzweil equations. Here again, the solutions of a QSDE are functions of bounded variation, that is they have the same properties as the Kurzweil equations associated with QSDEs introduced in [1, 4]. This generalizes similar results for classical initial value problems to the noncommutative quantum setting.

Last modified: 2014-02-07 15:13:24