Exponential decay of correlations for a real valued dynamical system embedded in $\mathbb R^2$

TL;DR

This paper investigates the decay of correlations in a real-valued dynamical system defined by a second-order recurrence relation, establishing conditions under which correlations diminish exponentially.

Contribution

It provides new theoretical results on exponential decay of correlations for a class of nonlinear second-order dynamical systems with bounded states.

Findings

Proves exponential decay of correlations under certain regularity conditions

Establishes bounds on the rate of decay

Provides a framework for analyzing similar dynamical systems

Abstract

We study the real valued process $ \{X_t, t\in {\mathbb N}\} $ defined by $X_{t+2} = \varphi(X_t,X_{t+1})$, where the $X_t$ are bounded. We aim at proving the decay of correlations for this model, under regularity assumptions on the transformation $\varphi$.