Potential Well Spectrum and Hitting Time in Renewal Processes

Mar 09, 2017

Miguel Abadi, Liliam Cardeño and Sandro Gallo

The potential well of a state can be interpreted physically as the energy that a stationary process needs to leave the state. We prove that for discrete time renewal processes, the potential well is the right scaling for the hitting and return time distributions of the state. We further detail the potential well spectrum of these processes by giving a complete classification of the states according to their potential well.

The whole paper is available here.

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