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Stationary distributions for jump processes with memory

K. Burdzy; T. Kulczycki; R. L. Schilling — 2012

Annales de l'I.H.P. Probabilités et statistiques

We analyze a jump processes $Z$ with a jump measure determined by a “memory” process $S$ . The state space of $(Z, S)$ is the Cartesian product of the unit circle and the real line. We prove that the stationary distribution of $(Z, S)$ is the product of the uniform probability measure and a Gaussian distribution.

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