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Limit distributions of some integral functionals for null-recurrent diffusions

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  • Khasminskii, R.

Abstract

The limit distributions as T-->[infinity] of the functional are found for one-dimensional null-recurrent Markov processes X(t) under different assumptions concerning local characteristics of X(t) and f. The conditions for the convergence of the distribution of this functional to each distribution in the class of generalized arc-sine law, studied by Lamperti and Watanabe, are obtained.

Suggested Citation

  • Khasminskii, R., 2001. "Limit distributions of some integral functionals for null-recurrent diffusions," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 1-9, March.
    • Handle: RePEc:eee:spapps:v:92:y:2001:i:1:p:1-9
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    Cited by:

    1. R. Höpfner & Yu. Kutoyants, 2003. "On a Problem of Statistical Inference in Null Recurrent Diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 25-42, January.
    2. Reinhard Höpfner & Carina Zeller, 2018. "LAMN in a class of parametric models for null recurrent diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 399-413, July.
    3. Löcherbach, Eva & Loukianova, Dasha, 2008. "On Nummelin splitting for continuous time Harris recurrent Markov processes and application to kernel estimation for multi-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1301-1321, August.
    4. D. Loukianova & O. Loukianov, 2008. "Deterministic equivalents of additive functionals of recurrent diffusions and drift estimation," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 107-121, June.

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