Deviations from Gaussianity in deterministic discrete time dynamical systems

Abstract

In this paper we examine the deviations from Gaussianity for two types of random variable converging to a normal distribution, namely sums of random variables generated by a deterministic discrete time map and a linearly damped variable driven by a deterministic map. We demonstrate how Edgeworth expansions provide a universal description of the deviations from the limiting normal distribution. We derive explicit expressions for these asymptotic expansions and provide numerical evidence of their accuracy.

References in corpus (3)

• Edgeworth expansions for weakly dependent random variables
• Edgeworth expansions for slow-fast systems with finite time scale separation
• Stochastic differential equations driven by deterministic chaotic maps: analytic solutions of the Perron-Frobenius equation

Cited by in corpus (1)

• The Emergence of the Normal Distribution in Deterministic Chaotic Maps