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

Author

Listed:
  • Yuling Tang
  • Caishi Wang
  • Suling Ren
  • Jinshu Chen

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.

Suggested Citation

  • Yuling Tang & Caishi Wang & Suling Ren & Jinshu Chen, 2019. "Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-8, January.
    • Handle: RePEc:hin:jnlamp:9382079
    DOI: 10.1155/2019/9382079
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