Stochastic Analysis and Applications

On computational procedures for weak solutions of quantum stochastic differential equations

E. O. Ayoola

Published Mar 21, 2002• 1 citation

Abstract

A continuous time Euler approximation scheme and a computational theorem for weak solutions of Lipschitzian quantum stochastic differential equations (QSDEs) are established. The work is accomplished within the framework of the Hudson–Parthasarathy formulation of quantum stochastic calculus and subject to the equivalent forms of the equations satisfying the Caratheodory conditions. Our results generalize analogous results concerning classical Ito stochastic differential equations and those of differential equations in a Banach space context to the noncommutative quantum setting involving unbounded linear operators on a Hilbert space. Numerical examples are given.

DOI: 10.1081/sap-120002419

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