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On transition density functions of skew Brownian motions with two-valued drift

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  • Lou, Shuwen

Abstract

In this article, based on the results in Gairat and Shcherbakov (2017), we derive two-sided bounds for the full family of transition density functions of skew Brownian motion (SBM in abbreviation) with two-valued drift for all t>0. As an important step of this result, it is also shown in this paper that SBM with two-valued drift is a strong Markov process by finding its symmetrizing measure and canonical scale function, from which one can tell what values of the drift make such a process transient or recurrent.

Suggested Citation

  • Lou, Shuwen, 2023. "On transition density functions of skew Brownian motions with two-valued drift," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002255
    DOI: 10.1016/j.spl.2022.109712
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    References listed on IDEAS

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    1. Alexander Gairat & Vadim Shcherbakov, 2017. "Density Of Skew Brownian Motion And Its Functionals With Application In Finance," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1069-1088, October.
    2. Lou, Shuwen, 2019. "Brownian motion with drift on spaces with varying dimension," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2086-2129.
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