Functional limit theorem for occupation time processes of intermittent maps

TL;DR

This paper proves a comprehensive limit theorem describing the joint behavior of occupation times and waiting times near indifferent fixed points in interval maps, extending classical arcsine laws and Darling--Kac theorems.

Contribution

It introduces a functional joint-law limit theorem for occupation and waiting times in intermittent maps, extending classical results to a joint and functional setting.

Findings

Established a strong distributional convergence for occupation and waiting times.

Extended classical arcsine laws to a joint, functional context.

Unified various limit theorems into a comprehensive framework.

Abstract

We establish a functional limit theorem for the joint-law of occupations near and away from indifferent fixed points of interval maps, and of waits for the occupations away from these points, in the sense of strong distributional convergence. It is a functional and joint-distributional extension of Darling--Kac type limit theorem, of Lamperti type generalized arcsine laws for occupation times, and of Dynkin and Lamperti type generalized arcsine laws for waiting times, at the same time.