Nous étudions le comportement asymptotique des maxima d'une classe générale de processus chaotiques déterministes – comprenant les applications tent et logistique –, de processus chaotiques bruités et des processus longue mémoire gaussiens de Gegenbauer à k facteurs.
We investigate the asymptotic behavior of the maxima of a general class of deterministic chaotic processes – including the tent map and the logistic map –, of noisy chaotic processes, and of the Gaussian long memory k-factor Gegenbauer processes.
Révisé le :
Publié le :
@article{CRMATH_2002__335_1_73_0, author = {Gu\'egan, Dominique and Ladoucette, Sophie}, title = {Extreme values of particular non-linear processes}, journal = {Comptes Rendus. Math\'ematique}, pages = {73--78}, publisher = {Elsevier}, volume = {335}, number = {1}, year = {2002}, doi = {10.1016/S1631-073X(02)02431-7}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02431-7/} }
TY - JOUR AU - Guégan, Dominique AU - Ladoucette, Sophie TI - Extreme values of particular non-linear processes JO - Comptes Rendus. Mathématique PY - 2002 SP - 73 EP - 78 VL - 335 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02431-7/ DO - 10.1016/S1631-073X(02)02431-7 LA - en ID - CRMATH_2002__335_1_73_0 ER -
%0 Journal Article %A Guégan, Dominique %A Ladoucette, Sophie %T Extreme values of particular non-linear processes %J Comptes Rendus. Mathématique %D 2002 %P 73-78 %V 335 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02431-7/ %R 10.1016/S1631-073X(02)02431-7 %G en %F CRMATH_2002__335_1_73_0
Guégan, Dominique; Ladoucette, Sophie. Extreme values of particular non-linear processes. Comptes Rendus. Mathématique, Tome 335 (2002) no. 1, pp. 73-78. doi : 10.1016/S1631-073X(02)02431-7. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02431-7/
[1] Limit theorems for the maximum term in stationary sequences, Ann. Math. Statist., Volume 35 (1964), pp. 502-516
[2] An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, New York, 1971
[3] Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proc. Cambridge Phil. Soc., Volume 24 (1928), pp. 180-190
[4] A generalized fractionally differencing approach in long memory modeling, Lithuanian Math. J., Volume 35 (1995), pp. 65-81
[5] Sur la distribution limité du terme d'une série aléatoire, Ann. Math., Volume 44 (1943), pp. 423-453
[6] Long memory behavior for simulated chaotic time series, IEICE Trans. Fund. E, Volume 84-A (2001), pp. 2145-2154
[7] D. Guégan, S. Ladoucette, Invariant measures and second order properties for maps on [0,1], Preprint 01.07, University of Reims, France, 2001
[8] D. Guégan, S. Ladoucette, Extremal behavior of particular non-linear processes, Preprint 02.01, GRID, ENS Cachan, France, 2002
[9] Properties of distributions and correlation integrals for generalized versions of the logistic map, Stochastics Process Appl., Volume 77 (1998), pp. 123-137
[10] Estimating the parameters of rare events, Stochastics Process Appl., Volume 37 (1991), pp. 117-139
[11] Statistical aspects of curved chaotic map models and their stochastic reversals, Scand. J. Statist., Volume 25 (1998), pp. 371-382
[12] Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, Berlin, 1983
[13] On the concept of complexity in random dynamical systems, Phys. Rev. E, Volume 53 (1996), pp. 2087-2098
[14] A k-factor GARMA long memory model, J. Time Ser. Anal., Volume 19 (1998), pp. 485-504
Cité par Sources :