Fluctuation scaling limits for positive recurrent jumping-in diffusions with large jumps

Abstract

For positive recurrent jumping-in diffusions with large jumps, we study scaling limits of the fluctuations of inverse local times and occupation times. We generalize the eigenfunctions with modified Neumann boundary condition, which have been introduced in the previous study for small jumps, to a class of diffusions of stronger singularity.

32 pages. arXiv admin note: text overlap with arXiv:1907.07925