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.
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