Stationary distributions for jump processes with inert drift

2010/09/13 by Burdzy, Krzysztof, Kulczycki, Tadeusz, Schilling, Rene
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1009.2347

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.

Related

• Stationary distributions for jump processes with memory
• Stationary fluctuations of run-and-tumble particles
• Processes with inert drift
• Stationary distributions for diffusions with inert drift
• Markov processes with product-form stationary distribution