Stationary random walks with a switch

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• Vladislav Vysotskiy (University of Sussex)
• Wednesday 14 August 2024, 15:00-16:00
• Seminar Room 2, Newton Institute.

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SSD - Stochastic systems for anomalous diffusion

A switching random walk, commonly known under the misnomer `oscillating random walk’, is a real-valued Markov chain whose distribution of increments depends only on the sign of the current position. Such chains are closely related to reflected random walks on the positive half-line. We find an invariant measure for a switching random walk and prove its uniqueness within the class of locally finite measures in a number of cases, including where the switching walk is recurrent. In the particular case where the switching walk is an actual random walk, our proof establishes a natural relationship between stationarity of the walk relative to the Lebesgue measure and stationarity of the renewal processes of its ascending and descending ladder heights, a classical result of the renewal theory.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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