Stable CLT for deterministic systems

TL;DR

This paper proves that for any ergodic, aperiodic measure-preserving system, one can construct functions whose time series converge in distribution to a symmetric alpha-stable law, extending classical limit theorems.

Contribution

It establishes a stable central limit theorem for deterministic systems, showing the existence of functions with stable law convergence in a broad ergodic setting.

Findings

Existence of functions with stable law limits in ergodic systems

Extension of CLT to deterministic systems with stable laws

Applicable for all alpha in (0,2)

Abstract

We show that for every ergodic and aperiodic probability preserving transformation and $\alpha\in (0,2)$ there exists a function whose associated time series is in the standard domain of attraction of a non-degenerate symmetric $\alpha$-stable distribution.