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

## TL;DR

This paper investigates the fluctuation limits of inverse local times and occupation times in positive recurrent jumping-in diffusions with small jumps, using eigenfunctions and Krein-Kotani correspondence.

## Contribution

It introduces a new approach with eigenfunctions and Krein-Kotani correspondence to analyze fluctuation limits in jumping-in diffusions.

## Key findings

- Distributional limits of fluctuations are established.
- Eigenfunctions with modified Neumann boundary conditions are utilized.
- The Krein-Kotani correspondence is applied to the analysis.

## Abstract

For positive recurrent jumping-in diffusions with small jumps, we establish distributional limits of the fluctuations of inverse local times and occupation times. For this purpose, we introduce and utilize eigenfunctions with modified Neumann boundary condition and apply the Krein-Kotani correspondence.