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