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On Dynamical Systems Perturbed by a Null-Recurrent Fast Motion: The Continuous Coefficient Case with Independent Driving Noises

Author

Listed:
  • Zsolt Pajor-Gyulai

    (University of Maryland, College Park)

  • Michael Salins

    (University of Maryland, College Park)

Abstract

An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these solutions from the averaged motion are studied, and a central limit type theorem is proved. The limit process satisfies a linear equation driven by a Brownian motion time changed by the local time of the fast motion.

Suggested Citation

  • Zsolt Pajor-Gyulai & Michael Salins, 2016. "On Dynamical Systems Perturbed by a Null-Recurrent Fast Motion: The Continuous Coefficient Case with Independent Driving Noises," Journal of Theoretical Probability, Springer, vol. 29(3), pages 1083-1099, September.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:3:d:10.1007_s10959-015-0600-5
    DOI: 10.1007/s10959-015-0600-5
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    References listed on IDEAS

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    1. Freidlin, M. I. & Wentzell, A. D., 2004. "Diffusion processes on an open book and the averaging principle," Stochastic Processes and their Applications, Elsevier, vol. 113(1), pages 101-126, September.
    2. Khasminskii, R. & Krylov, N., 2001. "On averaging principle for diffusion processes with null-recurrent fast component," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 229-240, June.
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