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On a Brownian motion with a hard membrane

Author

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  • Mandrekar, Vidyadhar
  • Pilipenko, Andrey

Abstract

Local perturbations of a Brownian motion are considered. As a limit we obtain a non-Markov process that behaves as a reflecting Brownian motion on the positive half line until its local time at zero reaches some exponential level, then changes a sign and behaves as a reflecting Brownian motion on the negative half line until some stopping time, etc.

Suggested Citation

  • Mandrekar, Vidyadhar & Pilipenko, Andrey, 2016. "On a Brownian motion with a hard membrane," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 62-70.
    • Handle: RePEc:eee:stapro:v:113:y:2016:i:c:p:62-70
    DOI: 10.1016/j.spl.2016.02.005
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    Cited by:

    1. Forien, Raphaël, 2019. "Gene flow across geographical barriers — scaling limits of random walks with obstacles," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3748-3773.

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