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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Acknowledgements
K. Burdzy was supported in part by NSF grant DMS-0906743 and by grant N N201 397137, MNiSW, Poland. T. Kulczycki was supported in part by grant N N201 373136, MNiSW, Poland. R.L. Schilling was supported in part by DFG grant Schi 419/5–1.
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Dedicated to David Nualart
Received 4/8/2011; Accepted 9/6/2011; Final 1/30/2012
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Burdzy, K., Kulczycki, T., Schilling, R.L. (2013). Stationary Distributions for Jump Processes with Inert Drift. In: Viens, F., Feng, J., Hu, Y., Nualart , E. (eds) Malliavin Calculus and Stochastic Analysis. Springer Proceedings in Mathematics & Statistics, vol 34. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5906-4_7
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