Excursions from Hyperplanes for Isotropic Stable Processes

在从原点的径向偏移中打破R中各向同性Lévy过程的路径是一种技术，用于理解过程接近原点或单位球S ={公式= 1 }时的行为。我们的目标是建立在这些想法和技术的基础上，并考虑与超平面H = {formulas =0 }相关的行为，其中v / S，并使用相关的路径分解来解决问题，例如如何使过程保持在超平面的一侧，检查最接近H的点，通过黎曼流形的共形变换，条件化永远不接触超平面或超平面与球面之间的关系。

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.