Stationary Distributions for Jump Processes with Inert Drift

  • K. BurdzyEmail author
  • T. Kulczycki
  • R. L. Schilling
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)


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.



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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Institute of MathematicsPolish Academy of SciencesWrocławPoland
  3. 3.Institute of Mathematics and Computer ScienceWrocław University of TechnologyWrocławPoland
  4. 4.Institut für StochastikTU DresdenDresdenGermany

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