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Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales

Suling Ren (), Yuling Tang (), Jinshu Chen () and Caishi Wang ()

Advances in Mathematical Physics, 2019, vol. 2019, 1-8

Abstract: Let be a discrete-time normal martingale satisfying some mild conditions. Then Gel’fand triple can be constructed of functionals of , where elements of are called testing functionals of , while elements of are called generalized functionals of . In this paper, we consider a quantum stochastic cable equation in terms of operators from to . Mainly with the 2D-Fock transform as the tool, we establish the existence and uniqueness of a solution to the equation. We also examine the continuity of the solution and its continuous dependence on initial values.

Date: 2019
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DOI: 10.1155/2019/9382079

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