A Coupling Method for Quantum Markov Processes
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Beschreibung
In classical probability theory the coupling method has established itself as a fruitful tool to analyse the ergodic behaviour of Markov processes, especially those without any stationary distribution. The thesis introduces this method to quantum probability theory. Moreover, it provides a scheme to apply the coupling method to tensor dilations, a class that frequently occurs in physical applications. It is shown that for asymptotically complete tensor dilations the coupling inequality yields sufficient estimates for the asymptotic loss of memory of the initial state of the process.
In classical probability theory the coupling method has established itself as a fruitful tool to analyse the ergodic behaviour of Markov processes, especially those without any stationary distribution. The thesis introduces this method to quantum probability theory. Moreover, it provides a scheme to apply the coupling method to tensor dilations, a class that frequently occurs in physical applications. It is shown that for asymptotically complete tensor dilations the coupling inequality yields sufficient estimates for the asymptotic loss of memory of the initial state of the process.
Autor*in
Kay Schwieger