Stationary distributions for jump processes with inert drift

Krzysztof Burdzy; Tadeusz Kulczycki; Rene Schilling

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arXiv · 1009.2347

Stationary distributions for jump processes with inert drift

Krzysztof Burdzy·Tadeusz Kulczycki·Rene Schilling

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Abstract

We analyze jump processes $Z$ with ``inert drift'' 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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Krzysztof Burdzy, Tadeusz Kulczycki, Rene Schilling. 2010-09-13. Stationary distributions for jump processes with inert drift. https://arxiv.org/abs/1009.2347

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