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Statistics of bounded processes driven by Poisson white noise

Author

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  • Denisov, S.I.
  • Bystrik, Yu.S.

Abstract

We study the statistical properties of jump processes in a bounded domain that are driven by Poisson white noise. We derive the corresponding Kolmogorov–Feller equation and provide a general representation for its stationary solutions. Exact stationary solutions of this equation are found and analyzed in two particular cases. All our analytical findings are confirmed by numerical simulations.

Suggested Citation

  • Denisov, S.I. & Bystrik, Yu.S., 2019. "Statistics of bounded processes driven by Poisson white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 38-46.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:38-46
    DOI: 10.1016/j.physa.2018.09.158
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    References listed on IDEAS

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    1. S. I. Denisov & W. Horsthemke & P. Hänggi, 2009. "Generalized Fokker-Planck equation: Derivation and exact solutions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 68(4), pages 567-575, April.
    2. S. I. Denisov & H. Kantz, 2011. "Probability distribution function for systems driven by superheavy-tailed noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 80(2), pages 167-175, March.
    3. Weiss, George H. & Szabo, Attila, 1983. "First passage time problems for a class of master equations with separable kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(3), pages 569-579.
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    Cited by:

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