Lyapunov Densities For Markov Processes: An Application To Quantum Systems With Non-Demolition Measurements

• URL: http://arxiv.org/abs/2402.12257v1
• Date: Mon, 19 Feb 2024 16:14:35 GMT
• Title: Lyapunov Densities For Markov Processes: An Application To Quantum Systems With Non-Demolition Measurements
• Authors: \"Ozkan Karabacak, Horia Cornean, Rafael Wisniewski
• Abstract summary: We show that existence of a properly subinvariant function implies sweeping of a Markov process out of the sets where this function is integrable. We apply this technique to Markov processes induced by a quantum system with non-demolition measurement.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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