# zbMATH — the first resource for mathematics

## Rio, Emmanuel

Compute Distance To:
 Author ID: rio.emmanuel Published as: Rio, E.; Rio, Emmanuel Homepage: http://lmv.math.cnrs.fr/annuaire/emmanuel-rio/ External Links: ResearchGate
 Documents Indexed: 51 Publications since 1993, including 3 Books
all top 5

#### Co-Authors

 32 single-authored 7 Merlevède, Florence 5 Dedecker, Jérôme 3 Massart, Pascal 2 Bercu, Bernard 2 Doukhan, Paul 2 Louhichi, Sana 2 Peligrad, Magda 1 Del Moral, Pierre 1 Delyon, Bernard 1 Gassiat, Elisabeth 1 Klein, Timo 1 Liu, Quansheng 1 Rouault, Alain
all top 5

#### Serials

 7 The Annals of Probability 7 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Probability Theory and Related Fields 6 Electronic Communications in Probability 4 Electronic Journal of Probability 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Theoretical Probability 2 Stochastic Processes and their Applications 2 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 The Annals of Applied Probability 1 Mathématiques & Applications (Berlin) 1 Probability Theory and Stochastic Modelling 1 SpringerBriefs in Mathematics
all top 5

#### Fields

 50 Probability theory and stochastic processes (60-XX) 9 Statistics (62-XX) 1 Number theory (11-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH

48 Publications have been cited 867 times in 653 Documents Cited by Year
Asymptotic theory of weakly dependent stochastic processes. Zbl 0944.60008
Rio, Emmanuel
2000
Invariance principles for absolutely regular empirical processes. Zbl 0817.60028
Doukhan, Paul; Massart, Pascal; Rio, Emmanuel
1995
The functional central limit theorem for strongly mixing processes. Zbl 0790.60037
Doukhan, Paul; Massart, Pascal; Rio, Emmanuel
1994
Concentration around the mean for maxima of empirical processes. Zbl 1066.60023
Klein, T.; Rio, E.
2005
The functional law of the iterated logarithm for stationary strongly mixing sequences. Zbl 0833.60024
Rio, Emmanuel
1995
On the functional central limit theorem for stationary processes. Zbl 0949.60049
Dedecker, Jérôme; Rio, Emmanuel
2000
Covariance inequalities for strongly mixing processes. Zbl 0798.60027
Rio, Emmanuel
1993
A Bernstein type inequality and moderate deviations for weakly dependent sequences. Zbl 1242.60020
Merlevède, Florence; Peligrad, Magda; Rio, Emmanuel
2011
About the Berry-Esseen theorem for weakly dependent sequences. Zbl 0838.60017
Rio, Emmanuel
1996
Bernstein inequality and moderate deviations under strong mixing conditions. Zbl 1243.60019
Merlevède, Florence; Peligrad, Magda; Rio, Emmanuel
2009
About the Lindeberg method for strongly mixing sequences. Zbl 0869.60021
Rio, Emmanuel
1995
A maximal inequality and dependent Marcinkiewicz-Zygmund strong laws. Zbl 0836.60026
Rio, Emmanuel
1995
Local invariance principles and their application to density estimation. Zbl 0794.60019
Rio, Emmanuel
1994
Upper bounds for minimal distances in the central limit theorem. Zbl 1175.60020
Rio, Emmanuel
2009
Hoeffding inequalities for Lipschitz functions of dependent sequences. Zbl 0961.60032
Rio, Emmanuel
2000
Moment inequalities for sums of dependent random variables under projective conditions. Zbl 1160.60312
Rio, Emmanuel
2009
Concentration inequalities for sums and martingales. Zbl 1337.60002
Bercu, Bernard; Delyon, Bernard; Rio, Emmanuel
2015
Une inégalité de Bennett pour les maxima de processus empiriques. (A Bennet type inequality for maxima of empirical processes). Zbl 1014.60011
Rio, Emmanuel
2002
Concentration inequalities for set-indexed empirical processes. Zbl 0976.60033
Rio, Emmanuel
2001
Strong approximation for set-indexed partial sum processes via KMT constructions. I. Zbl 0776.60045
Rio, Emmanuel
1993
Strong approximation of partial sums under dependence conditions with application to dynamical systems. Zbl 1230.60034
Merlevède, Florence; Rio, Emmanuel
2012
On mean central limit theorems for stationary sequences. Zbl 1187.60015
Dedecker, Jérôme; Rio, Emmanuel
2008
Asymptotic constants for minimal distance in the central limit theorem. Zbl 1225.60047
Rio, Emmanuel
2011
Absolutely regular empirical processes and universal entropy. Zbl 0911.60010
Rio, Emmanuel
1998
Rates of convergence for minimal distances in the central limit theorem under projective criteria. Zbl 1191.60025
Dedecker, Jérôme; Merlevède, Florence; Rio, Emmanuel
2009
Functional convergence to stable Lévy motions for iterated random Lipschitz mappings. Zbl 1245.60041
Louhichi, Sana; Rio, Emmanuel
2011
Concentration inequalities for mean field particle models. Zbl 1234.60019
Del Moral, Pierre; Rio, Emmanuel
2011
Moment inequalities for stationary and strongly mixing sequences. Zbl 0797.60011
Rio, Emmanuel
1994
Strong approximation for set-indexed partial-sum processes, via KMT constructions. II. Zbl 0779.60030
Rio, Emmanuel
1993
Extensions of the Hoeffding-Azuma inequalities. Zbl 1300.60036
Rio, Emmanuel
2013
Minimal distances and ideal distances. Zbl 0916.60015
Rio, Emmanuel
1998
Asymptotic theory of weakly dependent random processes. Translated from the French. Updated and extended translation. Zbl 1378.60003
Rio, Emmanuel
2017
Strong approximation for additive functionals of geometrically ergodic Markov chains. Zbl 1327.60085
Merlevède, Florence; Rio, Emmanuel
2015
Strong approximation of the empirical distribution function for absolutely regular sequences in $${\mathbb R}^d$$. Zbl 1293.60043
Dedecker, Jérôme; Rio, Emmanuel; Merlevède, Florence
2014
On McDiarmid’s concentration inequality. Zbl 1348.60042
Rio, Emmanuel
2013
Strong approximation results for the empirical process of stationary sequences. Zbl 1284.60069
Dedecker, Jérôme; Merlevède, Florence; Rio, Emmanuel
2013
Concentration inequalities, large and moderate deviations for self-normalized empirical processes. Zbl 1021.60013
Bercu, Bernard; Gassiat, Elisabeth; Rio, Emmanuel
2002
Limit theorems for multiplicative processes. Zbl 1039.60035
Liu, Quansheng; Rio, Emmanuel; Rouault, Alain
2003
A uniform Marcinkiewicz-Zygmund strong law of large numbers for empirical processes. Zbl 0933.60015
Massart, P.; Rio, E.
1998
About the rate function in Talagrand’s inequality for empirical processes. Zbl 1238.60024
Rio, Emmanuel
2012
Exponential inequalities for empirical processes. Zbl 0955.62051
Rio, Emmanuel
2000
Strong approximation for set-indexed partial sum processes via KMT constructions. III. Zbl 0930.60016
Rio, Emmanuel
1997
Rates of convergence in the strong law for dependent sequences. Zbl 0832.60042
Rio, Emmanuel
1995
About the constants in the Fuk-Nagaev inequalities. Zbl 1364.60029
Rio, Emmanuel
2017
New deviation inequalities for martingales with bounded increments. Zbl 1373.60049
Rio, Emmanuel
2017
Exponential inequalities for weighted sums of bounded random variables. Zbl 1328.60054
Rio, Emmanuel
2015
Convergence of partial sum processes to Lévy processes for associated sequences. Zbl 1213.60089
Louhichi, Sana; Rio, Emmanuel
2011
Rates of convergence in the invariance principle for the multivariate distribution function. Zbl 0837.60020
Rio, Emmanuel
1996
Asymptotic theory of weakly dependent random processes. Translated from the French. Updated and extended translation. Zbl 1378.60003
Rio, Emmanuel
2017
About the constants in the Fuk-Nagaev inequalities. Zbl 1364.60029
Rio, Emmanuel
2017
New deviation inequalities for martingales with bounded increments. Zbl 1373.60049
Rio, Emmanuel
2017
Concentration inequalities for sums and martingales. Zbl 1337.60002
Bercu, Bernard; Delyon, Bernard; Rio, Emmanuel
2015
Strong approximation for additive functionals of geometrically ergodic Markov chains. Zbl 1327.60085
Merlevède, Florence; Rio, Emmanuel
2015
Exponential inequalities for weighted sums of bounded random variables. Zbl 1328.60054
Rio, Emmanuel
2015
Strong approximation of the empirical distribution function for absolutely regular sequences in $${\mathbb R}^d$$. Zbl 1293.60043
Dedecker, Jérôme; Rio, Emmanuel; Merlevède, Florence
2014
Extensions of the Hoeffding-Azuma inequalities. Zbl 1300.60036
Rio, Emmanuel
2013
On McDiarmid’s concentration inequality. Zbl 1348.60042
Rio, Emmanuel
2013
Strong approximation results for the empirical process of stationary sequences. Zbl 1284.60069
Dedecker, Jérôme; Merlevède, Florence; Rio, Emmanuel
2013
Strong approximation of partial sums under dependence conditions with application to dynamical systems. Zbl 1230.60034
Merlevède, Florence; Rio, Emmanuel
2012
About the rate function in Talagrand’s inequality for empirical processes. Zbl 1238.60024
Rio, Emmanuel
2012
A Bernstein type inequality and moderate deviations for weakly dependent sequences. Zbl 1242.60020
Merlevède, Florence; Peligrad, Magda; Rio, Emmanuel
2011
Asymptotic constants for minimal distance in the central limit theorem. Zbl 1225.60047
Rio, Emmanuel
2011
Functional convergence to stable Lévy motions for iterated random Lipschitz mappings. Zbl 1245.60041
Louhichi, Sana; Rio, Emmanuel
2011
Concentration inequalities for mean field particle models. Zbl 1234.60019
Del Moral, Pierre; Rio, Emmanuel
2011
Convergence of partial sum processes to Lévy processes for associated sequences. Zbl 1213.60089
Louhichi, Sana; Rio, Emmanuel
2011
Bernstein inequality and moderate deviations under strong mixing conditions. Zbl 1243.60019
Merlevède, Florence; Peligrad, Magda; Rio, Emmanuel
2009
Upper bounds for minimal distances in the central limit theorem. Zbl 1175.60020
Rio, Emmanuel
2009
Moment inequalities for sums of dependent random variables under projective conditions. Zbl 1160.60312
Rio, Emmanuel
2009
Rates of convergence for minimal distances in the central limit theorem under projective criteria. Zbl 1191.60025
Dedecker, Jérôme; Merlevède, Florence; Rio, Emmanuel
2009
On mean central limit theorems for stationary sequences. Zbl 1187.60015
Dedecker, Jérôme; Rio, Emmanuel
2008
Concentration around the mean for maxima of empirical processes. Zbl 1066.60023
Klein, T.; Rio, E.
2005
Limit theorems for multiplicative processes. Zbl 1039.60035
Liu, Quansheng; Rio, Emmanuel; Rouault, Alain
2003
Une inégalité de Bennett pour les maxima de processus empiriques. (A Bennet type inequality for maxima of empirical processes). Zbl 1014.60011
Rio, Emmanuel
2002
Concentration inequalities, large and moderate deviations for self-normalized empirical processes. Zbl 1021.60013
Bercu, Bernard; Gassiat, Elisabeth; Rio, Emmanuel
2002
Concentration inequalities for set-indexed empirical processes. Zbl 0976.60033
Rio, Emmanuel
2001
Asymptotic theory of weakly dependent stochastic processes. Zbl 0944.60008
Rio, Emmanuel
2000
On the functional central limit theorem for stationary processes. Zbl 0949.60049
Dedecker, Jérôme; Rio, Emmanuel
2000
Hoeffding inequalities for Lipschitz functions of dependent sequences. Zbl 0961.60032
Rio, Emmanuel
2000
Exponential inequalities for empirical processes. Zbl 0955.62051
Rio, Emmanuel
2000
Absolutely regular empirical processes and universal entropy. Zbl 0911.60010
Rio, Emmanuel
1998
Minimal distances and ideal distances. Zbl 0916.60015
Rio, Emmanuel
1998
A uniform Marcinkiewicz-Zygmund strong law of large numbers for empirical processes. Zbl 0933.60015
Massart, P.; Rio, E.
1998
Strong approximation for set-indexed partial sum processes via KMT constructions. III. Zbl 0930.60016
Rio, Emmanuel
1997
About the Berry-Esseen theorem for weakly dependent sequences. Zbl 0838.60017
Rio, Emmanuel
1996
Rates of convergence in the invariance principle for the multivariate distribution function. Zbl 0837.60020
Rio, Emmanuel
1996
Invariance principles for absolutely regular empirical processes. Zbl 0817.60028
Doukhan, Paul; Massart, Pascal; Rio, Emmanuel
1995
The functional law of the iterated logarithm for stationary strongly mixing sequences. Zbl 0833.60024
Rio, Emmanuel
1995
About the Lindeberg method for strongly mixing sequences. Zbl 0869.60021
Rio, Emmanuel
1995
A maximal inequality and dependent Marcinkiewicz-Zygmund strong laws. Zbl 0836.60026
Rio, Emmanuel
1995
Rates of convergence in the strong law for dependent sequences. Zbl 0832.60042
Rio, Emmanuel
1995
The functional central limit theorem for strongly mixing processes. Zbl 0790.60037
Doukhan, Paul; Massart, Pascal; Rio, Emmanuel
1994
Local invariance principles and their application to density estimation. Zbl 0794.60019
Rio, Emmanuel
1994
Moment inequalities for stationary and strongly mixing sequences. Zbl 0797.60011
Rio, Emmanuel
1994
Covariance inequalities for strongly mixing processes. Zbl 0798.60027
Rio, Emmanuel
1993
Strong approximation for set-indexed partial sum processes via KMT constructions. I. Zbl 0776.60045
Rio, Emmanuel
1993
Strong approximation for set-indexed partial-sum processes, via KMT constructions. II. Zbl 0779.60030
Rio, Emmanuel
1993
all top 5

#### Cited by 734 Authors

 36 Dedecker, Jérôme 29 Merlevède, Florence 21 Doukhan, Paul 21 Peligrad, Magda 20 Comte, Fabienne 17 Rio, Emmanuel 11 Cuny, Christophe 11 Fan, Xiequan 11 Wu, Wei Biao 10 Genon-Catalot, Valentine 10 Sunklodas, Jonas Kazys 9 Neumann, Michael H. 9 Prieur, Clémentine 9 Volný, Dalibor 7 Grama, Ion G. 7 Liu, Quansheng 6 Belomestny, Denis 6 El Machkouri, Mohamed 6 Kato, Kengo 6 Lacour, Claire 6 Sancetta, Alessio 6 Wintenberger, Olivier 6 Zähle, Henryk 5 Ango Nze, Patrick 5 Bobkov, Sergey Germanovich 5 Bücher, Axel 5 Louhichi, Sana 5 Shao, Qi-Man 5 Utev, Sergey 4 Adamczak, Radosław 4 Alquier, Pierre 4 Arcones, Miguel A. 4 Berkes, István 4 Bousquet, Olivier 4 Bradley, Richard C. jun. 4 Chagny, Gaëlle 4 Chernozhukov, Victor 4 Chetverikov, Denis 4 Dehling, Herold G. 4 Durieu, Olivier 4 Fan, Jianqing 4 Guillin, Arnaud 4 Hill, Jonathan B. 4 Hu, Shuhe 4 Jirak, Moritz 4 Lang, Gabriel 4 León, José Rafael R. 4 Linton, Oliver Bruce 4 Lugosi, Gábor 4 Marchina, Antoine 4 Massart, Pascal 4 Melbourne, Ian 4 Mikosch, Thomas 4 Munk, Axel 4 Nickl, Richard 4 Pène, Françoise 4 Proksch, Katharina 4 Radulović, Dragan 4 Reynaud-Bouret, Patricia 4 Yang, Wenzhi 3 Alnafisah, Yousef 3 Baraud, Yannick 3 Bardet, Jean-Marc 3 Barigozzi, Matteo 3 Bartlett, Peter L. 3 Boucheron, Stéphane Vincent 3 Cai, Zongwu 3 Chen, Xiaohong 3 Chen, Xiaohui 3 Chesneau, Christophe 3 Davis, Richard A. 3 Del Moral, Pierre 3 Gassiat, Elisabeth 3 Giné-Masdéu, Evarist 3 Giraudo, Davide 3 Gouëzel, Sébastien 3 Hörmann, Siegfried 3 Jakubowski, Adam 3 Jiang, Binyan 3 Korepanov, Alexey 3 Kristensen, Dennis 3 Liebscher, Eckhard 3 Lin, Zhengyan 3 Mason, David M. 3 Mendelson, Shahar 3 Nicol, Matthew 3 Oliveira, Paulo Eduardo 3 Otsu, Taisuke 3 Ould-Saïd, Elias 3 Proïa, Frédéric 3 Segers, Johan 3 Seo, Myunghwan 3 Surgailis, Donatas 3 Taupin, Marie-Luce 3 Trapani, Lorenzo 3 Van de Geer, Sara Anna 3 Wang, Xuejun 3 Whang, Yoon-Jae 3 Wu, Liming 3 Xue, Liugen ...and 634 more Authors
all top 5

#### Cited in 119 Serials

 62 Stochastic Processes and their Applications 40 Journal of Econometrics 39 Statistics & Probability Letters 38 Bernoulli 33 The Annals of Probability 32 The Annals of Statistics 30 Journal of Statistical Planning and Inference 23 Journal of Multivariate Analysis 21 Journal of Theoretical Probability 18 Probability Theory and Related Fields 18 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 18 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 18 Electronic Journal of Statistics 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 13 Econometric Theory 11 Lithuanian Mathematical Journal 10 Statistics 9 Journal of Mathematical Analysis and Applications 9 The Annals of Applied Probability 9 Journal of Nonparametric Statistics 9 Stochastics and Dynamics 7 Mathematical Methods of Statistics 7 Statistical Inference for Stochastic Processes 6 Journal of Applied Probability 5 Metrika 5 Annals of the Institute of Statistical Mathematics 5 Transactions of the American Mathematical Society 5 Science China. Mathematics 4 Communications in Statistics. Theory and Methods 4 Journal of the Korean Statistical Society 3 Communications in Mathematical Physics 3 Journal of Statistical Physics 3 Acta Applicandae Mathematicae 3 Statistical Papers 3 Electronic Communications in Probability 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 3 Sankhyā. Series A 3 Dependence Modeling 2 Rocky Mountain Journal of Mathematics 2 Scandinavian Journal of Statistics 2 International Journal of Mathematics and Mathematical Sciences 2 Proceedings of the American Mathematical Society 2 SIAM Journal on Control and Optimization 2 Insurance Mathematics & Economics 2 Journal of Time Series Analysis 2 Stochastic Analysis and Applications 2 Acta Mathematicae Applicatae Sinica. English Series 2 Neural Computation 2 Computational Statistics 2 Computational Statistics and Data Analysis 2 Test 2 Applied Mathematics. Series B (English Edition) 2 Electronic Journal of Probability 2 Brazilian Journal of Probability and Statistics 2 Journal of Machine Learning Research (JMLR) 2 Statistical Methods and Applications 2 Applications and Applied Mathematics 2 Journal of Statistical Theory and Practice 1 Advances in Applied Probability 1 Communications on Pure and Applied Mathematics 1 Information Processing Letters 1 Israel Journal of Mathematics 1 Mathematical Notes 1 Nonlinearity 1 Periodica Mathematica Hungarica 1 Russian Mathematical Surveys 1 Chaos, Solitons and Fractals 1 Theory of Probability and its Applications 1 Advances in Mathematics 1 Applied Mathematics and Computation 1 Automatica 1 Inventiones Mathematicae 1 Journal of the American Statistical Association 1 Journal of Computational and Applied Mathematics 1 Journal of Functional Analysis 1 Mathematics of Operations Research 1 Memoirs of the American Mathematical Society 1 Theoretical Computer Science 1 Ergodic Theory and Dynamical Systems 1 Probability and Mathematical Statistics 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of Complexity 1 Journal of the American Mathematical Society 1 Journal of Scientific Computing 1 Machine Learning 1 Economics Letters 1 Journal of Statistical Computation and Simulation 1 Pattern Recognition 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Theory of Probability and Mathematical Statistics 1 Journal of Convex Analysis 1 Monte Carlo Methods and Applications 1 Annals of Mathematics and Artificial Intelligence 1 Lifetime Data Analysis 1 Discrete and Continuous Dynamical Systems 1 The Journal of Fourier Analysis and Applications 1 Doklady Mathematics 1 Abstract and Applied Analysis 1 Taiwanese Journal of Mathematics ...and 19 more Serials
all top 5

#### Cited in 30 Fields

 427 Probability theory and stochastic processes (60-XX) 374 Statistics (62-XX) 37 Dynamical systems and ergodic theory (37-XX) 34 Numerical analysis (65-XX) 25 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 19 Computer science (68-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Measure and integration (28-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Partial differential equations (35-XX) 4 Real functions (26-XX) 4 Functional analysis (46-XX) 4 Systems theory; control (93-XX) 4 Information and communication theory, circuits (94-XX) 3 Combinatorics (05-XX) 3 Number theory (11-XX) 3 Operations research, mathematical programming (90-XX) 2 Approximations and expansions (41-XX) 2 Operator theory (47-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX)