Comptes Rendus
no. 11
Dynamical systems
Exponential decay of correlations for a real-valued dynamical system embedded in R2
[Décroissance des corrélations pour une récurrence à deux termes]

Présenté par : the Editorial Board

Lisette Jager1 ; Jules Maes1 ; Alain Ninet1
1 Laboratoire de mathématiques, FR CNRS 3399, EA 4535, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1041-1045.

We study the real valued process {Xt,t∈N} defined by Xt+2=φ(Xt,Xt+1), where the Xt are bounded. We aim at proving the decay of correlations for this model, under regularity assumptions on the transformation φ.

On étudie le processus réel {Xt,t∈N} défini par Xt+2=φ(Xt,Xt+1), les Xt étant bornés. Sous des hypothèses de régularité sur la transformation φ, on établit la décroissance des corrélations pour ce modèle.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.07.015

Lisette Jager 1 ; Jules Maes 1 ; Alain Ninet 1

1 Laboratoire de mathématiques, FR CNRS 3399, EA 4535, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims, France 
@article{CRMATH_2015__353_11_1041_0,
     author = {Lisette Jager and Jules Maes and Alain Ninet},
     title = {Exponential decay of correlations for a real-valued dynamical system embedded in $ {\mathbb{R}}^{2}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1041--1045},
     publisher = {Elsevier},
     volume = {353},
     number = {11},
     year = {2015},
     doi = {10.1016/j.crma.2015.07.015},
     language = {en},
}
TY  - JOUR
AU  - Lisette Jager
AU  - Jules Maes
AU  - Alain Ninet
TI  - Exponential decay of correlations for a real-valued dynamical system embedded in $ {\mathbb{R}}^{2}$
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 1041
EP  - 1045
VL  - 353
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crma.2015.07.015
LA  - en
ID  - CRMATH_2015__353_11_1041_0
ER  - 
%0 Journal Article
%A Lisette Jager
%A Jules Maes
%A Alain Ninet
%T Exponential decay of correlations for a real-valued dynamical system embedded in $ {\mathbb{R}}^{2}$
%J Comptes Rendus. Mathématique
%D 2015
%P 1041-1045
%V 353
%N 11
%I Elsevier
%R 10.1016/j.crma.2015.07.015
%G en
%F CRMATH_2015__353_11_1041_0
Lisette Jager; Jules Maes; Alain Ninet. Exponential decay of correlations for a real-valued dynamical system embedded in $ {\mathbb{R}}^{2}$. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1041-1045. doi : 10.1016/j.crma.2015.07.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.07.015/

[1] J.F. Alves; J.M. Freitas; S. Luzatto; S. Vaienti From rates of mixing to recurrence times via large deviations, Adv. Math., Volume 228 (2011) no. 2, pp. 1203-1236

[2] P. Collet; J.-P. Eckmann Concepts and Results in Chaotic Dynamics: A Short Course, Theoretical and Mathematical Physics, Springer-Verlag, Berlin, 2006

[3] F. Hofbauer; G. Keller Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Z., Volume 180 (1982), pp. 119-140

[4] C.T. Ionescu Tulcea; G. Marinescu Théorie ergodique pour des classes d'opérations non complètement continues, Ann. of Math. (2), Volume 52 (1950), pp. 140-147

[5] A. Lasota; M.C. Mackey Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Springer Verlag, New York, 1998

[6] C. Liverani Multidimensional expanding maps with singularities: a pedestrian approach, Ergod. Theory Dyn. Syst., Volume 33 (2013) no. 1, pp. 168-182

[7] B. Saussol Absolutely continuous invariant measures for multidimensional expanding maps, Isr. J. Math., Volume 116 (2000), pp. 223-248

[8] H. Tong Nonlinear Time Series: A Dynamical System Approach (with an appendix by K.S. Chan), Oxford Statistical Science Series, vol. 6, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1990

[9] H. Tong Nonlinear time series analysis since 1990: some personal reflections, Acta Math. Appl. Sin. Engl. Ser., Volume 18 (2002) no. 2, pp. 177-184

[10] L.-S. Young Recurrence times and rates of mixing, Isr. J. Math., Volume 110 (1999), pp. 153-188

  • Lisette Jager; Jules Maes; Alain Ninet Exponential Decay of Correlations for a Real-Valued Dynamical System Generated by a k k Dimensional System, Acta Applicandae Mathematicae, Volume 160 (2019) no. 1, p. 21 | DOI:10.1007/s10440-018-0192-z
  • Hanyuan Hang; Ingo Steinwart A Bernstein-type inequality for some mixing processes and dynamical systems with an application to learning, The Annals of Statistics, Volume 45 (2017) no. 2 | DOI:10.1214/16-aos1465

Cité par 2 documents. Sources : Crossref

Commentaires - Politique