Excursions from Hyperplanes for Isotropic Stable Processes

打破各向同性lsamvy过程在R中从原点径向偏移的路径是一种技术，用于理解过程在接近原点或单位球S ={formulae = 1}时的行为。我们的目标是建立在这些理念和技术,并考虑相关行为与超平面H ={公式= 0},与v / S,并使用相关的路径分解来解决这样的问题如何条件过程保持超平面的一侧,检查最近的达到H,空调不要接触超平面或之间的关系和黎曼流形的球面通过保角变换情况。

Breaking the paths of isotropic Lévy processes in R in radial excursions from the origin is a technique that has been used to understand the behaviour of processes when they approach the origin or the unit sphere S ={formulae = 1 }. We aim to build on these ideas and techniques and consider related behaviour in relation to the hyperplane H = {formulae =0 }, with v / S, and use the associated path decomposition to address questions such as how to condition the process to stay on one side of the hyperplane, examining the point of closest reach to H, conditioning to never touch the hyperplane or the relationship between this and the spherical case via conformal transformations of Riemannian manifolds.