2024/02/19 by Özkan Karabacak, Karabacak, Özkan, Horia D. Cornean +3
Mathematics · Physics and Astronomy · #93D05 #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2402.12257
openalex publication_date 2024/02/19 · openalex created_date 2024/02/21 · openalex updated_date 2026/07/28
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.