Diffusion and Generation of Non-Gaussianity in Chaotic Discrete Dynamics

Abstract

In this contribution we discuss the long-time dynamics of Y_t [1–4] governed by

$${Y_{t + 1}}\, = \,{Y_t}\, + \,\Delta ({x_t})\,,\,(t = 0,1,2, \cdots )\,,\,{Y_0} = 0$$

(1.1)

where Δ is a certain steady stochastic variable generated by a chaotic variable x_t obeying a one-dimensional map

$${X_{t + 1}}\, = \,f({x_t})\,,\,(0\, \leqslant \,{x_t}\, < \,1\,).$$

(1.2)