On dynamical systems perturbed by a null-recurrent fast motion: the continuous coefficient case with independent driving noises
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Citation (published version)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, Volume 29, Issue 3, pp. 1083 - 1099 (17). https://doi.org/10.1007/s10959-015-0600-5
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.