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On quasi-ergodic distribution for one-dimensional diffusions

Author

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  • He, Guoman
  • Zhang, Hanjun

Abstract

In this paper, we study quasi-ergodicity for one-dimensional diffusion X killed at 0, when 0 is an exit boundary and +∞ is an entrance boundary. Using the spectral theory tool, we show that if the killed semigroup is intrinsically ultracontractive, then there exists a unique quasi-ergodic distribution for X. An example is given to illustrate the result. Moreover, the ultracontractivity of the killed semigroup is also studied.

Suggested Citation

  • He, Guoman & Zhang, Hanjun, 2016. "On quasi-ergodic distribution for one-dimensional diffusions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 175-180.
    • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:175-180
    DOI: 10.1016/j.spl.2015.12.026
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    References listed on IDEAS

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    1. Chen, Jinwen & Jian, Siqi, 2014. "A remark on quasi-ergodicity of ultracontractive Markov processes," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 184-190.
    2. Breyer, L. A. & Roberts, G. O., 1999. "A quasi-ergodic theorem for evanescent processes," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 177-186, December.
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    Cited by:

    1. He, Guoman & Zhang, Hanjun & Zhu, Yixia, 2019. "On the quasi-ergodic distribution of absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 116-123.
    2. He, Guoman & Zhang, Hanjun & Yang, Gang, 2021. "Exponential mixing property for absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 179(C).

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