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

TL;DR

This paper investigates the fluctuation limits of inverse local times and occupation times in positive recurrent jumping-in diffusions with large jumps, extending eigenfunction methods to more singular cases.

Contribution

It generalizes eigenfunction techniques with modified boundary conditions to analyze fluctuation limits in diffusions with stronger singularities and large jumps.

Findings

Derived fluctuation scaling limits for inverse local times.

Extended eigenfunction methods to more singular diffusions.

Provided theoretical framework for large jump regimes.

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.