Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales
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 con...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/9382079 |
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| author | Yuling Tang Caishi Wang Suling Ren Jinshu Chen |
| author_facet | Yuling Tang Caishi Wang Suling Ren Jinshu Chen |
| author_sort | Yuling Tang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-91b9a249781247fa86d8f02c4a76794b |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-91b9a249781247fa86d8f02c4a76794b2025-02-03T01:25:23ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/93820799382079Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal MartingalesYuling Tang0Caishi Wang1Suling Ren2Jinshu Chen3School of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaSchool of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaSchool of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaSchool of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaLet 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.http://dx.doi.org/10.1155/2019/9382079 |
| spellingShingle | Yuling Tang Caishi Wang Suling Ren Jinshu Chen Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales Advances in Mathematical Physics |
| title | Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales |
| title_full | Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales |
| title_fullStr | Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales |
| title_full_unstemmed | Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales |
| title_short | Quantum Stochastic Cable Equation Acting on Functionals of Discrete-Time Normal Martingales |
| title_sort | quantum stochastic cable equation acting on functionals of discrete time normal martingales |
| url | http://dx.doi.org/10.1155/2019/9382079 |
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