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

Yuling Tang, Caishi Wang, Suling Ren and Jinshu Chen

Advances in Mathematical Physics, 2019, vol. 2019, issue 1

Abstract: Let M be a discrete‐time normal martingale satisfying some mild conditions. Then Gel’fand triple S(M)⊂L2(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.

Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2019/9382079

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:9382079

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().