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A density for the local time of the Brox diffusion

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  • Gutierrez-Pavón, Jonathan
  • Pacheco, Carlos G.

Abstract

We give explicitly the probability density of the local time of the Brox diffusion at first passage times. Such formula is used to find the moments and to relate the minima and maxima of the environment to the most and least visited points of the diffusion.

Suggested Citation

  • Gutierrez-Pavón, Jonathan & Pacheco, Carlos G., 2020. "A density for the local time of the Brox diffusion," Statistics & Probability Letters, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:stapro:v:163:y:2020:i:c:s0167715220300948
    DOI: 10.1016/j.spl.2020.108791
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    References listed on IDEAS

    as
    1. Cheliotis, Dimitris, 2008. "Localization of favorite points for diffusion in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1159-1189, July.
    2. Shi, Zhan, 1998. "A local time curiosity in random environment," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 231-250, August.
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    Cited by:

    1. Gutierrez-Pavón, Jonathan & Pacheco, Carlos G., 2022. "Quenched distributions for the maximum, minimum and local time of the Brox diffusion," Statistics & Probability Letters, Elsevier, vol. 180(C).

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