Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales. (1st January 2019)

• Record Type: Journal Article
• Authors: Tang, Yuling; Wang, Caishi; Ren, Suling; Chen, Jinshu
• Other Names: Salahshour Soheil Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2019(2019)
• Publication Date: 2019-01-01
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2019/9382079
• Languages: English
• ISSNs: 1687-9120

Abstract

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.