Matching of observations of dynamical systems, with applications to sequence matching - IRD - Institut de recherche pour le développement Access content directly
Journal Articles Physica D Year : 2022

Matching of observations of dynamical systems, with applications to sequence matching

Abstract

We study the statistical distribution of the closest encounter between generic smooth observations computed along dierent trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of Gumbel type that depends on both the length of the trajectories and on the Generalized Dimensions of the image measure. It is also modulated by an Extremal Index, that informs on the tendency of nearby observations to diverge along with the evolution of the dynamics. We give a formula for this quantity for a class of chaotic maps of the interval and regular observations. We present diverse numerical applications illustrating the theory and discuss the implications of these results for the study of physical systems. Finally, we discuss the connection between this problem and the problem of the longest matching block common to dierent sequences of symbols. In particular, we obtain a distributional result for strongly mixing processes.
Fichier principal
Vignette du fichier
newobsf - Copie.pdf (484.05 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

ird-03725164 , version 1 (15-07-2022)

Identifiers

Cite

Théophile Caby. Matching of observations of dynamical systems, with applications to sequence matching. Physica D, In press. ⟨ird-03725164⟩
108 View
71 Download

Altmetric

Share

Gmail Facebook X LinkedIn More