Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales. (1st January 2019) - Tang, Yuling; Wang, Caishi; Ren, Suling; Chen, Jinshu
Abstract : Let M be a discrete-time normal martingale satisfying some mild conditions. Then Gel'fand triple S ( M ) ⊂ L 2 ( M ) ⊂ S ⁎ ( M ) can be constructed of functionals of M, where elements of S ( M ) are called testing functionals of M, while elements of S ⁎ ( M ) are called generalized functionals of M . In this paper, we consider a quantum stochastic cable equation in terms of operators from S ( M ) to S ⁎ ( M ) . 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.