论文标题
限制性的马雀问题和最佳条件的本地化，以反映二维域扩散的独特性
Localization for constrained martingale problems and optimal conditions for uniqueness of reflecting diffusions in 2-dimensional domains
论文作者
论文摘要
我们证明了半明星的存在和唯一性，反映在二维分段平滑域中扩散的，在几何，易于证实的条件下，每个“侧面”的反射方向变化，倾斜的反射方向变化。我们的条件是最佳的，从某种意义上说，在凸多边形的情况下，两侧的反射恒定方向，它们还原为Dai and Williams（1996）的条件，这对于反映布朗尼运动的存在是必不可少的。此外，我们的条件允许尖端。我们的论点是基于限制性的Martingale问题的新本地化结果，该结果通常存在：作为另一个例子，我们表明它适用于具有跳跃边界条件的扩散。
We prove existence and uniqueness for semimartingale reflecting diffusions in 2-dimensional piecewise smooth domains with varying, oblique directions of reflection on each "side", under geometric, easily verifiable conditions. Our conditions are optimal in the sense that, in the case of a convex polygon with constant direction of reflection on each side, they reduce to the conditions of Dai and Williams (1996), which are necessary for existence of Reflecting Brownian Motion. Moreover our conditions allow for cusps. Our argument is based on a new localization result for constrained martingale problems which holds quite generally: as an additional example, we show that it holds for diffusions with jump boundary conditions.
