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

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.