Invariance principle for local time by quasi-compactness

TL;DR

This paper establishes a functional weak invariance principle for the local time of certain measure-preserving dynamical systems with quasi-compact transfer operators, extending understanding of stochastic behavior in such systems.

Contribution

It proves a new invariance principle for local times in dynamical systems with quasi-compact transfer operators, broadening the scope of stochastic process approximations.

Findings

Proves a functional weak invariance principle for local time

Applies to systems with quasi-compact transfer operators

Extends stochastic process approximation in dynamical systems

Abstract

The objective of this paper is to prove a functional weak invariance principle for a local time of a process of the form $X_{n}=\varphi\circ T^{n}$ where $\left(X,\mathcal{B},T,m\right)$ is a measure preserving system with a transfer operator acting quasi-compactly on a large enough Banach space of functions and $\varphi\in L^{2}\left(m\right)$ is an aperiodic observable.