Professor
Team : Probability and Statistics
Contact :
Bâtiment Fermat, Bureau 2310
01 39 25 36 26
Curriculum Vitae
Personal Data
Place of birth : Paris, France. Citizenship : France.
Fields of research : Probability Theory and Stochastic Processes
– Strong approximations and applications to linear estimators
– Weak dependence, strongly mixing and β-mixing processes
– Martingales, martingale approximation, projective criteria
– Empirical processes : independent or weakly dependent data
– Probability inequalities, concentration inequalities
– Normal approximation
– Probability metrics and functional inequalities
– Positively dependent sequences : inequalities and functional convergence
Degrees and awards obtained
1990 : Ph. D., University Paris 11, Orsay
1994 : Habilitation à diriger des recherches, University Paris 11, Orsay
Professional experiences
1987-1990 : Assistant at the University Paris 11, Orsay.
1990-2000 : Researcher at CNRS (chargé de recherche), Orsay.
Since 2000 : Professor at the University of Versailles
Past Ph. D. Students
1. J. Dedecker, Ph. D. 1998, Professor at the University Paris Descartes.
2. T. Klein, Ph. D. 2003, MCF at the University Paul Sabatier, Toulouse.
3. A. Marchina, Ph. D. 2017, MCF at the University Paris Descartes.
List of Publications
Textbooks
1. Théorie asymptotique des processus aléatoires faiblement dépendants. Ed. J.M. Ghidaglia et X. Guyon. Mathématiques et Applications 31. Springer (2000).
2. with B. Bercu and B. Delyon. Concentration inequalities for sums and
martingales. SpringerBriefs in Mathematics. Springer (2015).
3. Asymptotic theory of weakly dependent random processes (translation
and second version of 1.). Probability Theory and Stochastic Modelling, 80. Springer (2017).
Articles
37. About Doob’s inequality, entropy and Tchebichef. Electron. Commun. Probab. 2018, Vol. 23, No 78, 1-12.
36. About the constants in the Fuk-Nagaev inequalities.
Electron. Commun. Probab. 2017, Vol. 22 No 28, 1-12.
35. New deviation inequalities for martingales with bounded increments.
Stochastic Processes and their Applications 2017, Vol. 137, No 5, 1637-1648.
34. Exponential inequalities for weighted sums of bounded random
variables. Electron. Commun. Probab. 2015, Vol. 20, No 77, 1-10.
33. with F. Merlevède. Strong approximation for additive functionals
of geometrically ergodic Markov chains.
Electron. J. Probab. 2015, Vol. 20, No 14, 1-27.
32. with J. Dedecker and F. Merlevède. Strong approximation of the empirical distribution function for absolutely regular sequences in R^d.
Electron. J. Probab. 2014, Vol. 19, No 9, 1-56.
31. with J. Dedecker and F. Merlevède. Strong approximation results for the empirical process of stationary sequences. Ann. Probab. 2013, Vol. 41, No 5, 3658-3696.
30. Extensions of the Hoeffding-Azuma inequalities.
Electron. Commun. Probab. 2013, Vol. 18, No 54, 1–6.
29. On McDiarmid’s concentration inequality.
Electron. Commun. Probab. 2013, Vol. 18, No 44, 1–11.
28. with F. Merlevède. Strong approximation of partial sums under dependence conditions with application to dynamical systems.
Stochastic Processes and their Applications 2012, Vol. 122, 386-417.
27. with F. Merlevède and M. Peligrad. A Bernstein type inequality and moderate deviations for weakly dependent sequences. Prob. Th. Rel. Fields. 2011, Vol. 151, 435-474
26. with S. Louhichi. Functional convergence to Lévy motions for iterated random Lipschitz mappings. Electron. J. Probab. 2011, Vol. 16, 2452-2480.
25. with P. Del Moral. Concentration inequalities for mean field particle models. Ann. Appl. Probab. 2011, Vol. 21. No 3, 1017-1052.
24. Asymptotic constants for minimal distances in the central limit theorem. Electron. Commun. Probab. 2011, Vol. 16, 96-103.
23. Upper bounds for minimal distances in the central limit theorem.
Ann. Inst. H. Poincaré Probab. Statist. 2009, Vol. 45, No 3, 802-817.
22. with J. Dedecker and F. Merlevède. Rates of convergence for minimal metrics in the central limit theorem under projective criteria. Electron. J. Probab. 2009, Vol. 14, 978-1011.
21. Moment inequalities for sums of dependent random variables under projective conditions. J. Theor. Probab. 2009, Vol. 22, No 1, 146-163.
20. with J. Dedecker. On Esseen’s mean central limit theorem for dependent sequences. Ann. Inst. H. Poincaré, Probab. Statist. 2008, Vol. 44, No 4, 693-726.
19. with T. Klein. Concentration around the mean for maxima of empirical processes. Ann. Probab. 2005, Vol. 33. No 3, 1060-1077.
18. with Q. Liu and A. Rouault. Limit theorems for multiplicative processes. J. Theor. Probab. 2003, Vol. 16, No 4, 971-1014.
17. with B. Bercu and E. Gassiat. Concentration inequalities, large and moderate deviations for self-normalized empirical processes. Ann. Probab. 2002, Vol. 30. No 4, 1576-1604.
16. Une inégalité de Bennett pour les maxima de processus empiriques. Ann. Institut H. Poincaré, Probab. Statist. 2002, Vol. 38, No 6, 1053-1057.
15. Inégalités de concentration pour les processus empiriques de classes de parties. Prob. Th. Rel. Fields, 2001, Vol. 119, 163-175.
14. Lois fortes des grands nombres presque sûres pour les sommes de
Riesz-Raikov. Prob. Th. Rel. Fields, 2000, Vol. 118, 342-348.
13. With J. Dedecker.On the functional central limit theorem for stationary processes. Ann. Inst. H. Poincaré, Probab. Statist. 2000, Vol. 36, No 1, 1-34.
12. Processus empiriques absolument réguliers et entropie universelle. Prob. Th. Rel. Fields, 1998, Vol. 111, 585-608.
11. Strong approximation for set-indexed partial-sum processes, via KMT constructions III. ESAIM Probab. Statist. 1997, Vol. 1, 319-338.
10. Sur le théorème de Berry-Esseen pour les suites faiblement dépendantes. Prob. Th. Rel. Fields 1996, Vol. 104, No 2, 255-282.
9. About the Lindeberg method for strongly mixing sequences. ESAIM Probab. Statist. 1995, Vol. 1, 35-61.
8. The functional law of the iterated logarithm for stationary strongly mixing sequences. Ann. Probab. 1995, Vol. 23. No 3, 1188-1203.
7. A maximal inequality and dependent Marcinkiewicz-Zygmund strong laws. Ann. Probab. 1995, Vol. 23, No 2, 918-937 .
6. with P. Doukhan and P. Massart. Invariance principles for absolutely regular empirical processes. Ann. Inst. H. Poincaré Probab. Statist. 1995, Vol. 31. No 2, 393-427.
5. with P. Doukhan and P. Massart. The functional central limit theorem for strongly mixing processes. Ann. Inst. H. Poincaré Probab. Statist. 1994, Vol. 30. No 1, 63-82.
4. Covariance inequalities for strongly mixing processes. Ann. Inst. H. Poincaré Probab. Statist. 1993, Vol 29, No 4, 587-597.
3. Local invariance principles and their application to density estimation. Prob. Th. Rel. Fields. 1994, Vol. 98, No 1, 21-45.
2. Strong approximation for set-indexed partial-sum processes, via KMT constructions II. Ann. Probab. 1993, Vol. 21, No 3, 1706-1727.
1. Strong approximation for set-indexed partial-sum processes, via KMT constructions I. Ann. Probab. 1993, Vol. 21, No 2, 759-790.
Conference proceedings
1. With F. Merlevède et M. Peligrad. Bernstein inequality and moderate deviations under strong mixing conditions. 273-292. High dimensional probability V. The Luminy Volume. IMS collections, Vol. 5. 2009.
Notes aux Comptes rendus Acad. Sci. Paris, Série I
9. About the conditional value at risk of partial sums. 2017.
T. 355, 1190-1195.
8. Sur la fonction de taux dans les inégalités de Talagrand pour les processus empiriques. 2012. T. 350, 303-305.
7. with S. Louhichi. Convergence du processus de sommes partielles vers un processus de Lévy pour les suites associées. 2011. T. 349, 89-91.
6. Inégalités de Hoeffding pour les fonctions lipschitziennes de suites dépendantes. 2000. T. 330, 905-908.
5. Inégalités exponentielles pour les processus empiriques. 2000. T. 330, 597-600.
4. Distances minimales et distances idéales. 1998. T. 326, 1127-1130.
3. Vitesse de convergence dans le principe d’invariance faible pour la fonction de répartition empirique multivariée. 1996. T. 322, 169-172.
2. Vitesses de convergence dans la loi forte pour des suites dépendantes. 1995, T. 320, 469-474.
1. Inégalités de moments pour les suites stationnaires et fortement mélangeantes. 1994, T. 318, 355-360.
Online courses
1. HAL : cel-00702524. Inégalités exponentielles et inégalités de concentration (22 pages). 2012.
2. HAL : cel-00867106. Inequalities and limit theorems for weakly dependent
sequences (170 pages). 2013.
Asymptotic Theory of Weakly Dependent Random Processes: corrections
– Preface to the French Edition, line 6: replace “la addition” by “l’addition”.
Line 22: replace “mont” by “m’ont”.
– Page 5, lines 12 and 13: The distribution function and the tail function are
right-continuous: replace “left-continuous” by “right-continuous”.
– Page 90, line 2 (in Lemma 5.1), line 14 (in Lemma 5.2) and page 98,
line 2 (in Lemma 5.4):
X* is independent of the sigma field A, but X* depends on X.
Consequently replace “independent of X” by “independent of A”.
– Page 135, line -3: The end of the phrase has been mistakenly removed by the Editor. Add “applications to classes of sets” after “lies in the”.
– Page 150, line -4: replace “L(x,A)” by “G(x,A)”.
– Page 151, line 2. Add “such that phi(A)>0” at the end of the second phrase
of Definition 9.3.
– Page 152, line 13. Replace “and Q(x,A) = …” by “and Q_1 (x,A) =…”
(et aussi dans la version de 2000, page 130, ligne 22).
– Page 156, line 10: replace “P(X)” by “P^n (X)”.
– Page 158, Proposition 9.4, line -3: replace (9.16) by (9.15) (et aussi
dans la version de 2000, page 136, ligne 3).
– Page 163, line -3: add “< ∞.” at the end of this line.
Concentration Inequalities for Sums and Martingales: corrections
– Page 14, Lemma 2.6 and lines 15-16 : The famous paper of Hoeffding (1963) does not contain this lemma. Consequently the reference to [11] shoud be removed.
– Page 19, line 15: replace “sharper than the first improvement of Bennett (2.25)” by “sharper than (2.4)”.
– Page 19, line 21: replace “sharper than (2.25)” by “sharper than (2.4)”.
– Page 38, line -1: replace “k=0” by “k=1” under the sign sum.