We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provides necessary and sufficient conditions for existence and uniqueness of a solution to the corresponding submartingale problem with drift, and show that its solution possesses the Markov and Feller properties. Next, we study a version of the problem with absorption at the vertex of the wedge. In this case, we provide a condition for existence and uniqueness of a solution to the problem and some results on the probability of the vertex being reached.

中文翻译：

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楔形漂移的反射布朗运动

我们研究了反映布朗运动的漂移被限制在平面上的楔子上。我们的第一组结果为相应的带有漂移的下鞅问题解的存在性和唯一性提供了充要条件，并表明其解具有马尔可夫和费勒性质。接下来，我们研究楔形顶点吸收问题的一个版本。在这种情况下，我们提供了问题解的存在性和唯一性的条件以及到达顶点的概率的一些结果。