Lyapunov Densities For Markov Processes: An Application To Quantum Systems With Non-Demolition Measurements
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909111598186496 |
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| author | Karabacak, Özkan Cornean, Horia Wisniewski, Rafael |
| author_facet | Karabacak, Özkan Cornean, Horia Wisniewski, Rafael |
| contents | Stochastic convergence of discrete time Markov processes has been analysed based on a dual Lyapunov approach. Using some existing results on ergodic theory of Markov processes, it has been shown that existence of a properly subinvariant function (counterpart of the Lyapunov density in deterministic systems) implies sweeping of a Markov process out of the sets where this function is integrable. Such a function can be used as a certificate of convergence in probability of a stochastic system. We apply this technique to Markov processes induced by a quantum system with non-demolition measurement and propose dual Lyapunov certificates to certify sweeping. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lyapunov Densities For Markov Processes: An Application To Quantum Systems With Non-Demolition Measurements Karabacak, Özkan Cornean, Horia Wisniewski, Rafael Dynamical Systems Quantum Physics 93D05 Stochastic convergence of discrete time Markov processes has been analysed based on a dual Lyapunov approach. Using some existing results on ergodic theory of Markov processes, it has been shown that existence of a properly subinvariant function (counterpart of the Lyapunov density in deterministic systems) implies sweeping of a Markov process out of the sets where this function is integrable. Such a function can be used as a certificate of convergence in probability of a stochastic system. We apply this technique to Markov processes induced by a quantum system with non-demolition measurement and propose dual Lyapunov certificates to certify sweeping. |
| title | Lyapunov Densities For Markov Processes: An Application To Quantum Systems With Non-Demolition Measurements |
| topic | Dynamical Systems Quantum Physics 93D05 |
| url | https://arxiv.org/abs/2402.12257 |