Converging multistep schemes for weak solutions of quantum stochastic differential equations |
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Authors: | E.O. Ayoola |
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Affiliation: | Department of Mathematics , University of Ibadan , Ibadan, Nigeria E-mail: eoayoola@email.com |
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Abstract: | Multistep schemes for computing weak solutions of Lipschitzian quantum stochastic differential equations (QSDE) driven by certain operator-valued stochastic processes associated with the basic field operators of quantum field theory are introduced and studied. This is accomplished within the framework of the Hudson–Parthasarathy formulation of quantum stochastic calculus and subject to matrix element of solution being sufficiently differentiable. Results concerning convergence of explicit schemes of class A in the topology of the locally convex space of solution are presented.Numerical examples are given. |
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Keywords: | QSDE 60H10 60H20 Boson Fock Spaces 65U05 65LO6 81S25 Exponential Vectors Tensor Product Sesquilinear Form Valued Maps Multistep Schemes Noncommutative Stochastic Processes |
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