Invited Speaker - Clémentine Prieur (Grenoble 1)

Title:

Measures of dependence : application to one-dimensional dynamical systems.

Abstract:

Even a simple and deterministic dynamical system may behave "impredictably". One says that the system presents a "chaotic" behavior. Choosing two initial conditions close to each other, one may observe, after a finite time, two orbits which are totally diferent. This motivates the study of the statistical properties of dynamical systems. We will introduce in this talk several measures of dependence [1] which will allow to derive interesting stochastic properties for two classes of one-dimensional expanding dynamical systems ([2],[3]).

References:


[1] Dedecker J. and Prieur C. (2005). New dependence coefficients. Examples and applications to statistics. Probab. Theory and Relat. Fields 132, p. 203-236.
[2] Dedecker J. and Prieur C. (2008). Some unbounded functions of intermittent maps for which the central limit theorem holds. ALEA 5, p. 29-45.
[3] Prieur C. (2006). Recent results on weak dependence for causal sequences, Statistical applications and dynamical systems' example. Lecture Notes in Stat. 187, p. 87-104.