Explicit Transition Density Functions of Skew Brownian Motions with Two-Valued Drift

Shuwen Lou

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arXiv · 2205.06902

Explicit Transition Density Functions of Skew Brownian Motions with Two-Valued Drift

Shuwen Lou

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Abstract

In this article, we derive the explicit 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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Shuwen Lou. 2022-05-13. Explicit Transition Density Functions of Skew Brownian Motions with Two-Valued Drift. https://arxiv.org/abs/2205.06902

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