mardi 9 mars 2010
par  Paul Doukhan

Recent Publications

- Books
- Publications in refereed journals
- Colloquia, congresses and chapters in a book
- Notes at Comptes Rendus Acad. Sc. Paris
- In preparation


[1] Mixing : properties and examples ; Lecture Notes in Statistics 85, Springer-Verlag, 1994.

[2] Theory and Applications of Long-range Dependence, Paul Doukhan, Georges Oppenheim and Murad S. Taqqu editors (718 pages) Birkhaüser, Boston (2003).

[3] Course of Mathematical Analysis with Jean Claude Sifre in French, Editions Dunod

[4] Dependence in Probability and Statistics , Patrice Bertail, Paul Doukhan, and Philippe Soulier (Editors.) Springer, New York (500 pages) 2006.

[5] Weak dependence : models, theory and applications (350 pages), Lecture Notes 190 in Statistics, Springer-Verlag, with G. Lang, C. Prieur, S. Louhichi, J. Dedecker, J. R. Leon (2007).

Publications in refereed journals

publications in reviews with a reading comity

[1] with M. Ghindes. Estimation de la transition de probabilité d’une chaîne de Markov Doëblin récurrente. Stoch. Proc. Appl. 15, 271-293 (1983).

[2] with F. Portal and J.R. Leon. Calcul de la vitesse de convergence dans le théorème central limite vis à vis des distances de Dudley, Lévy et Prokhorov. Probab. Math. Stat. 6.2, 19-27 (1985).

[3] with F. Portal, J.R. Leon. Une mesure de la déviation quadratique d’estimateurs non paramétriques. Ann. I.H.P. 22-1, 37-66 (1986).

[4] with F. Portal. Principe d’invariance faible pour la fonction de répartition empirique dans un cadre multidimensionnel et mélangeant. Probab. Math. Stat. 8.2, 117-132 (1987).

[5] with F. Portal, J.R. Leon. Principe d’invariance faible pour la mesure empirique d’une suite de variables aléatoires dépendantes. Probab. Th. Rel. Fields 76, 51-70 (1987).

[6] with J.R. Leon, J.L. Nicolle. Metodologia para evaluar la sismicidad cuando la base de datos es incompleta. Rev. Tec. I.N.T.E.V.E.P. 8.1, 13-22 (1988).

[7] with J.R. Leon. Cumulants for mixing sequences and applications to empirical spectral density. Probab. Math. Stat.10.1, 11-26 (1989).

[8] with E. Gassiat. Quadratic deviation of penalized mean square regression estimates. J. Mult. Anal. 41, 89-101 (1992).

[9] with J. Leon. Quadratic deviation of projection density estimates. Re. Bra. P. E. 7, 37-63 (1993).

[10] with P. Massart, E. Rio. The functional central limit theorem for weakly dependent processes. Ann. I.H.P. 30-1, 63-82 (1994).

[11] with A. Tsybakov. Estimation in non parametric A.R.X models. in Russian : Problemy Peredachi Informatsii, 24-34, 1993- Problems of Trans. of Inform. 29-4, 318-327 (1994).

[12] with P. Massart, E. Rio. Invariance principle for the empirical measure of a weakly dependent process. Ann. I.H.P. 31-2, 393-427 (1995).

[13] with P. Ango Nze. Non parametric Minimax estimation in a weakly dependent framework I : Quadratic properties. Math. Meth. Statist. 5-4, 404-423 (1996).

[14] with J. Leon and P. Soulier. Empirical periodogramm of a long range dependent stationary Gaussian random field. Re. Bra. P. E., 10-2, 205-223 (1996).

[15] with F. Gamboa. Prohorov rates in super-resolution. Canad. J. of Math., 48 (2), 316-329, (1996).

[16] with J. Leon. Asymptotics for the local time of a Gaussian random field. Period. Math. Hung. 70 (4), 329-351 (1996).

[17] with P. Ango Nze. Non parametric Minimax estimation in a weakly dependent framework II : Uniform properties. J. Stat. Plann. Inference 68, 5-29 (1998).

[18] An overview on weak dependence conditions of stationary sequences. Acta Cient. Venez. 49-2, 78-93 (1998).

[19] with S. Louhichi. A new weak dependence condition and applications to moment inequalities. Stoch. Proc. Appl. 84, 313-342 (1999).

[20] with C. Coulon-Prieur. A CLT for triangular arrays of weakly dependent sequences. Statist. Probab. Letters 47, 61-68 (2000).

[21] with S. Louhichi. Functional estimation for weakly dependent stationary time series. Scandinavian J. of Statistics 28-2, 325-342 (2001).

[22] with P. Ango Nze, P. Bühlmann. Weak dependence beyond mixing and asymptotics for non parametric regression. Ann. Statist. 30-2, 397-430 (2002).

[23] with G. Lang. Rates of convergence in the weak invariance principle for the empirical repartition process of weakly dependent sequences. Stat. Inf. for Stoch. Proc. 5, 199-228 (2002).

[24] with G. Lang, D. Surgailis. Functional CLTs for short or long memory linear sequences. Festschrift D. Dacunha-Castelle, J. Bretagnolle and I. Ibragimov. Special issue of Ann. I.H.P. B. 38-6, 879-896 (2002).

[25] with J. Dedecker. A new covariance inequality and applications.Stoch. Proc. Appl., Vol. 106 n°1, 63-80 (2003).

[26] with P. Ango Nze, Weak dependence, models and applications to econometrics. Econometric Theory, Volume 20, Number 6, 995-1045 (2004).

[27] with J. Leon. Asymptotics for L_p-deviation of a variance estimator under diffusion. ESAIM P&S 8, 132-149 (2004).

[28] with O. Brandière. Dependent noise for stochastic algorithms. Prob. Math. Stat. 26 (2), 153-171 (2004).

[29] with G. Lang, D. Surgailis, M. C. Viano. Functional limit theorem for the empirical process shifts with long memory. J. Theor. Probab. 18, 1, 109-134 (2005).

[30] with B. Ycart, Y. Coupier. 0-1 laws for dependent images, Alea (2006).

[31] with A. Latour and D. Oraichi. Simple integer-valued bilinear time series model. Advances in Applied Probabilty 38, 559-578 (2006).

[32] with H. Madré, M. Rosenbaum. ARCH type bilinear weakly dependent models, Statistics 41-1, 31-45 (2007).

[33] with M. Neumann. A Bernstein type inequality for times series, Stoch. Proc. Appl. 117-7,878-903 (2007).

[34] with O. Wintenberger. A central limit theorem under non causal weak dependence and sharp moment assumptions, Prob. Math. Stat. 27, 45-73. (2007)

[35] with J. M. Bardet, G. Lang, N. Ragache. A Lindeberg central limit theorem for dependent processes and its statistical applications, ESAIM P&S 12, 154-172 (2008).

[36] with G. Lang, D. Surgailis. Limit theorems for sums of non linear function of ARFIMA processes with random Hurst exponents and Gaussian innovations, Lith. J. of Math. 47-1, 1-25 (2007).

[37] with J. M. Bardet and J. R. Leon.A functional limit theorem for weakly dependent processes and its applications. Stat. Inf. Stoch. Proc (2007).

[38] with J. M. Bardet and J. R. Leon. A uniform central limit theorem for the periodogram and its applications to Whittle parametric estimation for weakly dependent time series, J.T.S.A.. (2008).

[39] with G. Lang, S. Louhichi, B. Ycart. A functional central limit theorem for interacting particle systems on transitive graphs. Markov Processes Relat. Fields 14, 79-114 (2008).

[40] with L. Truquet. A fixed point approach to model random fields. Alea 2, 111-132 (2007).

[41] with O. Wintenberger. Weakly dependent chains with infinite memory, Stoch. Proc. and Applic .(2008).

[42] with J. D. Fermanian, G. Lang. Copula of a stationary vector valued weakly dependent process, accepté, SISP.

[43] with M. Neumann. The notion of weak dependence and its applications to bootstrapping time series, Probab. Reviews (2008).

[44] with N. Mayo, L. Truquet. Weak dependence, models and some applications.Submitted to Metrika (2008).

Colloquia, congresses and chapters in a book

[1] Simulations in the general first order autoregressive process. Specifying statistical models, Louvain 1982, L.N. in Statistics 16, 50-68, (1983).

[2] Polynômes d’Hermite et statistique des processus mélangeants, Bruxelles 1985. Review of C.E.R.O., Bruxelles 28, 99-115 (1986).

[3] with J.R. Leon. Invariance principles for the empirical measure of a mixing sequence and for the local time of a Markov process. Geometrical and statistical aspects of probability in Banach spaces, Strasbourg 1985 ; L. N. M. 1993, 4-21, Springer (1986).

[4] Non parametric estimation of a regression function in a mixing framework. Caracas, Acta Cient. Venez. 38, 5-6, 585-590 (1987).

[5] Consistency of d-estimates for a regression or a density in a dependent framework in Séminaire de Statistiques d’Orsay 1989-1990 : Estimation Fonctionnelle. Preprint Orsay 91-55, 121-141 (1991).

[6] with J. R. Leon, S. Ben Hariz. Central Limit Theorem for the local time of a Gaussian random process. Dalang, Robert C. (ed.) et al., Seminar on Stochastic analysis, random fields and applications. Centro Stefano Franscini, Ascona, Italy, September 1996. Basel : Birkhäuser. Prog. Probab. 45, 25-37 (1999).

[7] with P. Ango Nze. Weak dependence : models and applications, Dehling W. (ed.) et al., Empirical Processes Techniques for Dependent Data, 117-137, Birkhaüser (2002).

[8] Models Inequalities and Limit Theorems for Stationary Sequences. 60 pages in Theory and Applications of Long-range Dependence (book[2]).

[9] with A. Khezour, G. Lang. Non-parametric estimation for LRD sequences. 10 pages in Theory and Applications of Long-range Dependence (book[2]).

[10] with G. Teyssière, P. Winant.. Vector valued ARCH infinity processes, in Dependence in Probability and Statistics. Patrice Bertail, Paul Doukhan and Philippe Soulier Editors, Springer, New York, (2006).

Notes at Comptes Rendus Acad. Sc. Paris

(with proofs and without any forthcoming publication)

[1] with M. Ghindes. Etude du processus Xn+1= f(Xn) + en. . C.R.A.S. Série A, 290, 921-923 (1980).

[2] with G. Collomb. Estimation non paramétrique de la fonction d’autorégression d’un processus stationnaire et f-mélangeant. C.R.A.S. Série 1, 296, 859-863, (1983).

[3] with F. Portal, J.R. Leon. Vitesse de convergence dans le théorème central limite pour des variables aléatoires mélangeantes à valeurs dans un espace de Hilbert. C.R.A.S. Série 1, 298, 305-308 (1984).

[4] with A. Bulinskii. Inégalités de mélange fort utilisant des normes d’Orlicz. C.R.A.S. Série 1, 305, 827-830 (1987).

[5] Formes de Toëplitz associées à une analyse multi-échelle. C.R.A.S. Série 1, 306, 663-666 (1988).

[6] with A. Bulinskii. Vitesse dans le théorème de limite centrale pour des champs mélangeants satisfaisant des hypothèses de moments faibles. C.R.A.S. Série 1, 311, 801-805 (1990).

[7] with X. Guyon. Mélange pour des processus linéaires spatiaux. C.R.A.S. Série 1, 313, 465-470 (1992).

[8] with D. Surgailis. Functional Central Limit Theorem for the empirical process of a short memory linear process. C.R.A.S. Série 1, 326, 87-92 (1998).

[9] with O. Brandière. Algorithmes stochastiques à bruit dépendant. C.R.A.S. Série 1, 337-7,473-476 (2003).

[10] with G. Teyssière, P. Winant.. Modèles ARCH infinis vectoriels, C.R.A.S. Série 1, 339 (2005).

In preparation

[1] with G. Lang,. Evaluation for moments of a ratio with application to regression estimation, Submitted.

[2] with G. Lang, O., Klesov. Rates in strong laws of large numbers in nonparametric statistics, in preparation.

[3] with J. Leon.. Subsampling an asymptotic variance, in preparation.

[4] with G. Lang, D. Surgailis. Limit theorems for non linear long range dependent Bernoulli shifts sequences, in preparation.

[5] with N. Ragache. A CLT for weakly dependent triangular arrays : application to functional estimation, in preparation.

[6] with O. Brandière. How to make the method of moments work ? Applications to random matrices, in preparation.

[7] with N. Bahamonde, E. Moulines. Spectral estimation for censored times series data, in preparation..

[8] with G. Lang. A dependent analogue to Kolmogorov Smirnov test, in preparation.

- Books
- Journal Articles
- colloquia, congresses and chapters in a book
- Notes at Comptes Rendus Acad. Sc. Paris
- In preparation