R. Adamczak, A tail inequality for suprema of unbounded empirical processes with applications to Markov chains, Electronic Journal of Probability, vol.13, issue.0, pp.1000-1034, 2008.
DOI : 10.1214/EJP.v13-521

K. Azuma, Weighted sums of certain dependent random variables, Tohoku Mathematical Journal, vol.19, issue.3, pp.357-367, 1967.
DOI : 10.2748/tmj/1178243286

Y. Baraud, Bounding the expectation of the supremum of an empirical process over a (weak) VC-major class, Electronic Journal of Statistics, vol.10, issue.2, pp.1709-1728, 2016.
DOI : 10.1214/15-EJS1055

URL : https://hal.archives-ouvertes.fr/hal-01085004

G. Bennett, Probability Inequalities for the Sum of Independent Random Variables, Journal of the American Statistical Association, vol.18, issue.297, pp.33-45, 1962.
DOI : 10.6028/NBS.RPT.1744

V. Bentkus, An inequality for tail probabilities of martingales with bounded differences, Liet. Mat. Rink, vol.42, issue.3, pp.323-331, 2002.

V. Bentkus, An inequality for tail probabilities of martingales with differences bounded from one side, Journal of Theoretical Probability, vol.16, issue.1, pp.161-173, 2003.
DOI : 10.1023/A:1022234622381

V. Bentkus, On Hoeffding?s inequalities, The Annals of Probability, vol.32, issue.2, pp.1650-1673, 2004.
DOI : 10.1214/009117904000000360

URL : http://doi.org/10.1214/009117904000000360

V. Bentkus, On measure concentration for separately Lipschitz functions in product spaces, Israel Journal of Mathematics, vol.31, issue.1, pp.1-17, 2007.
DOI : 10.1090/conm/234/03452

V. Bentkus, An extension of the Hoeffding inequality to unbounded random variables, Lithuanian Mathematical Journal, vol.31, issue.4, pp.137-157, 2008.
DOI : 10.1214/EJP.v11-371

V. Bentkus, Addendum to ???An extension of an inequality of Hoeffding to unbounded random variables???: The non-i.i.d. case, Lithuanian Mathematical Journal, vol.58, issue.2, pp.237-255, 2008.
DOI : 10.1007/978-0-387-34675-5

V. Bentkus, Bounds for the stop loss premium for unbounded risks under the variance constraints. Preprint on https, 2010.

V. Bentkus and D. Dzindzalieta, A tight Gaussian bound for weighted sums of Rademacher random variables, Bernoulli, vol.21, issue.2, pp.1231-1237, 2015.
DOI : 10.3150/14-BEJ603

V. Bentkus, N. Kalosha, and M. Zuijlen, On domination of tail probabilities of (super)martingales: Explicit bounds, Lithuanian Mathematical Journal, vol.31, issue.4, pp.1-43, 2006.
DOI : 10.1090/conm/234/03452

B. Bercu, B. Delyon, and E. Rio, Concentration Inequalities for Sums and Martingales, SpringerBriefs in Mathematics, 2015.
DOI : 10.1007/978-3-319-22099-4

URL : https://hal.archives-ouvertes.fr/hal-01256173

S. N. Bernstein, The theory of probabilities, 1946.

S. G. Bobkov, F. Götze, and C. Houdré, On Gaussian and Bernoulli Covariance Representations, Bernoulli, vol.7, issue.3, pp.439-451, 2001.
DOI : 10.2307/3318495

S. Boucheron, G. Lugosi, and P. Massart, Concentration Inequalities : A Nonasymptotic Theory of Independence
DOI : 10.1093/acprof:oso/9780199535255.001.0001

URL : https://hal.archives-ouvertes.fr/hal-00794821

O. Bousquet, Concentration Inequalities for Sub-Additive Functions Using the Entropy Method, Stochastic inequalities and applications, pp.213-247, 2003.
DOI : 10.1007/978-3-0348-8069-5_14

B. Courbot, Rates of convergence in the functional CLT for martingales, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.328, issue.6, pp.509-513, 1999.
DOI : 10.1016/S0764-4442(99)80200-6

D. P. Dubhashi and A. Panconesi, Concentration of measure for the analysis of randomized algorithms, 2009.
DOI : 10.1017/CBO9780511581274

M. L. Eaton, A Note on Symmetric Bernoulli Random Variables, The Annals of Mathematical Statistics, vol.41, issue.4, pp.1223-1226, 1970.
DOI : 10.1214/aoms/1177696897

URL : http://doi.org/10.1214/aoms/1177696897

M. L. Eaton, A Probability Inequality for Linear Combinations of Bounded Random Variables, The Annals of Statistics, vol.2, issue.3, pp.609-614, 1974.
DOI : 10.1214/aos/1176342725

L. J. Gleser, On the Distribution of the Number of Successes in Independent Trials, The Annals of Probability, vol.3, issue.1, pp.182-188, 1975.
DOI : 10.1214/aop/1176996461

W. Hoeffding, On the Distribution of the Number of Successes in Independent Trials, The Annals of Mathematical Statistics, vol.27, issue.3, pp.713-721, 1956.
DOI : 10.1214/aoms/1177728178

W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1007/BF02883985

T. Klein, Une in??galit?? de concentration ?? gauche pour les processus empiriques, Comptes Rendus Mathematique, vol.334, issue.6, pp.501-504, 2002.
DOI : 10.1016/S1631-073X(02)02303-8

T. Klein and E. Rio, Concentration around the mean for maxima of empirical processes, The Annals of Probability, vol.33, issue.3, pp.1060-1077, 2005.
DOI : 10.1214/009117905000000044

J. Lederer and S. Van-de-geer, New concentration inequalities for suprema of empirical processes, Bernoulli, vol.20, issue.4, pp.2020-2038
DOI : 10.3150/13-BEJ549

M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM: Probability and Statistics, vol.1, pp.63-87, 1997.
DOI : 10.1051/ps:1997103

URL : https://www.esaim-ps.org/10.1051/ps:1997103/pdf

M. Ledoux, The concentration of measure phenomenon, volume 89 of Mathematical Surveys and Monographs, 2001.

K. Marton, A simple proof of the blowing-up lemma (Corresp.), IEEE Transactions on Information Theory, vol.32, issue.3, pp.445-446, 1986.
DOI : 10.1109/TIT.1986.1057176

K. Marton, Bounding $\bar{d}$-distance by informational divergence: a method to prove measure concentration, The Annals of Probability, vol.24, issue.2, pp.857-866, 1996.
DOI : 10.1214/aop/1039639365

K. Marton, A measure concentration inequality for contracting markov chains, Geometric and Functional Analysis, vol.81, issue.158, pp.556-571, 1996.
DOI : 10.1007/BF02699376

P. Massart, empirical processes, The Annals of Probability, vol.28, issue.2, pp.863-884, 2000.
DOI : 10.1214/aop/1019160263

B. Maurey, Construction de suites symétriques, C. R. Acad. Sci. Paris Sér. A-B, vol.288, issue.14, pp.679-681, 1979.

C. Mcdiarmid, On the method of bounded differences, pp.148-188, 1989.
DOI : 10.1017/CBO9781107359949.008

C. Mcdiarmid, Concentration, Probabilistic methods for algorithmic discrete mathematics, pp.195-248, 1998.
DOI : 10.1007/978-3-662-12788-9_6

V. D. Milman and G. Schechtman, Asymptotic theory of finite dimensional normed spaces, Lecture Notes in Mathematics, vol.1200, 1986.

I. Pinelis, Extremal Probabilistic Problems and Hotelling's $T^2$ Test Under a Symmetry Condition, The Annals of Statistics, vol.22, issue.1, pp.357-368, 1994.
DOI : 10.1214/aos/1176325373

URL : http://doi.org/10.1214/aos/1176325373

I. Pinelis, Optimal Tail Comparison Based on Comparison of Moments, High dimensional probability, pp.297-314, 1998.
DOI : 10.1007/978-3-0348-8829-5_19

I. Pinelis, Fractional sums and integrals of r-concave tails and applications to comparison probability inequalities Advances in stochastic inequalities, pp.149-168, 1997.

I. Pinelis, Binomial upper bounds on generalized moments and tail probabilities of (super)martingales with differences bounded from above, High dimensional probability, pp.33-52, 2006.
DOI : 10.1214/074921706000000743

I. Pinelis, On normal domination of (super)martingales. Electron, J. Probab, vol.11, issue.39, pp.1049-1070, 2006.

I. Pinelis, Exact inequalities for sums of asymmetric random variables, with applications. Probability Theory and Related Fields, pp.605-635, 2007.

I. Pinelis, Toward the best constant factor for the Rademacher-Gaussian tail comparison, ESAIM: Probability and Statistics, vol.22, pp.412-426, 2007.
DOI : 10.1007/s00440-007-0055-4

I. Pinelis, On the Bennett???Hoeffding inequality, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.50, issue.1, 2009.
DOI : 10.1214/12-AIHP495

I. Pinelis, On the Bennett???Hoeffding inequality, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.50, issue.1, pp.15-27
DOI : 10.1214/12-AIHP495

URL : http://doi.org/10.1214/12-aihp495

I. Pinelis, An Optimal Three-Way Stable and Monotonic Spectrum of Bounds on Quantiles: A Spectrum of Coherent Measures of Financial Risk and Economic Inequality, Risks, vol.72, issue.4, pp.349-392, 2014.
DOI : 10.1007/BF01311347

I. Pinelis, Convex cones of generalized multiply monotone functions and the dual cones, Banach Journal of Mathematical Analysis, vol.10, issue.4, pp.864-897
DOI : 10.1215/17358787-3649788

I. Pinelis, Optimal binomial, Poisson, and normal left-tail domination for sums of nonnegative random variables, Electronic Journal of Probability, vol.21, 2016.
DOI : 10.1214/16-EJP4474

I. F. Pinelis and A. I. Sakhanenko, Remarks on Inequalities for Large Deviation Probabilities, Theory of Probability & Its Applications, vol.30, issue.1, pp.143-148, 1986.
DOI : 10.1137/1130013

E. Rio, Inégalités exponentielles pour les processus empiriques Comptes Rendus de l'Académie des Sciences -Series I -Mathematics, pp.597-600, 2000.
DOI : 10.1016/s0764-4442(00)00210-x

E. Rio, Inégalités de concentration pour les processus empiriques de classes de parties. Probab. Theory Related Fields, pp.163-175, 2001.
DOI : 10.1007/pl00008756

E. Rio, Une in??galit?? de Bennett pour les maxima de processus empiriquesA Bennet type inequality for maxima of empirical processes, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.38, issue.6, pp.1053-1057, 2002.
DOI : 10.1016/S0246-0203(02)01122-6

E. Rio, Sur la fonction de taux dans les in??galit??s de Talagrand pour les processus empiriques, Comptes Rendus Mathematique, vol.350, issue.5-6, pp.5-6303, 2012.
DOI : 10.1016/j.crma.2012.02.006

E. Rio, About the constants in the Fuk-Nagaev inequalities, Electronic Communications in Probability, vol.22, issue.0, p.12, 2017.
DOI : 10.1214/17-ECP57

P. Samson, Infimum-convolution description of concentration properties of product probability measures, with applications, Annales de l'Institut Henri Poincare (B) Probability and Statistics, pp.321-338, 2007.
DOI : 10.1016/j.anihpb.2006.05.003

URL : https://hal.archives-ouvertes.fr/hal-00693095

M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publications Mathematiques de l'IHES, pp.73-205, 1995.
DOI : 10.1137/1119012

M. Talagrand, New concentration inequalities in product spaces, Inventiones Mathematicae, vol.126, issue.3, pp.505-563, 1996.
DOI : 10.1007/s002220050108

M. Talagrand, A new look at independence. The Annals of probability, pp.1-34, 1996.
DOI : 10.1214/aop/1042644705

S. Van-de-geer and J. Lederer, The Bernstein-Orlicz norm and deviation inequalities. Probab. Theory Related Fields, pp.225-250, 2013.

L. Wu, Large Deviations, Moderate Deviations and LIL for Empirical Processes, The Annals of Probability, vol.22, issue.1, pp.17-27, 1994.
DOI : 10.1214/aop/1176988846

URL : http://doi.org/10.1214/aop/1176988846

V. V. Yurinskii, Exponential bounds for large deviations Theory of Probability & Its Applications References Remark 2.9.1. See that, contrary to (2.9.8), there is a F k?1 -measurable term in the expectation in the right-hand side of, pp.154-155, 1974.

]. R. References1 and . Adamczak, A tail inequality for suprema of unbounded empirical processes with applications to Markov chains, Electron. J. Probab, vol.13, issue.34, pp.1000-1034, 2008.

R. Adamczak and P. Wolff, Concentration inequalities for non-lipschitz functions with bounded derivatives of higher order. Probability Theory and Related Fields, pp.531-586, 2015.

V. Bentkus, On Hoeffding?s inequalities, The Annals of Probability, vol.32, issue.2, pp.1650-1673, 2004.
DOI : 10.1214/009117904000000360

URL : http://doi.org/10.1214/009117904000000360

V. Bentkus, An extension of the Hoeffding inequality to unbounded random variables, Lithuanian Mathematical Journal, vol.31, issue.4, pp.137-157, 2008.
DOI : 10.1214/EJP.v11-371

V. Bentkus, Addendum to ???An extension of an inequality of Hoeffding to unbounded random variables???: The non-i.i.d. case, Lithuanian Mathematical Journal, vol.58, issue.2, pp.237-255, 2008.
DOI : 10.1007/978-0-387-34675-5

V. Bentkus, Bounds for the stop loss premium for unbounded risks under the variance constraints. Preprint on https, 2010.

V. Bentkus, N. Kalosha, and M. Zuijlen, On domination of tail probabilities of (super)martingales: Explicit bounds, Lithuanian Mathematical Journal, vol.31, issue.4, pp.1-43, 2006.
DOI : 10.1090/conm/234/03452

B. Bercu, B. Delyon, and E. Rio, Concentration Inequalities for Sums and Martingales, SpringerBriefs in Mathematics, 2015.
DOI : 10.1007/978-3-319-22099-4

URL : https://hal.archives-ouvertes.fr/hal-01256173

S. Boucheron, O. Bousquet, G. Lugosi, and P. Massart, Moment inequalities for functions of independent random variables, The Annals of Probability, vol.33, issue.2, pp.514-560, 2005.
DOI : 10.1214/009117904000000856

URL : https://hal.archives-ouvertes.fr/hal-00101850

S. Boucheron, G. Lugosi, and P. Massart, Concentration Inequalities: A Nonasymptotic Theory of Independence
DOI : 10.1093/acprof:oso/9780199535255.001.0001

URL : https://hal.archives-ouvertes.fr/hal-00794821

M. Csörgö and L. Horváth, Weighted Approximations in Probability and Statistics, 1993.

L. Dümbgen, S. Van-de-geer, M. C. Veraar, and J. A. Wellner, Nemirovski's inequalities revisited. The American mathematical monthly, the official journal of the Mathematical Association of America, vol.117, issue.2, p.138, 2010.

T. Figiel, P. Hitczenko, W. B. Johnson, G. Schechtman, and J. Zinn, Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities, Transactions of the American Mathematical Society, vol.349, issue.03, pp.997-1027, 1997.
DOI : 10.1090/S0002-9947-97-01789-3

W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1007/BF02883985

T. Klein, Y. Ma, and N. Privault, Convex Concentration Inequalities and Forward-Backward Stochastic Calculus, Electronic Journal of Probability, vol.11, issue.0, pp.486-512, 2006.
DOI : 10.1214/EJP.v11-332

URL : http://www.amt.ac.cn/academic/workshop/workshop10/%C2%ED%D3%EE%E8%BA.pdf

A. Kontorovich, Concentration in unbounded metric spaces and algorithmic stability, ICML, pp.28-36, 2014.

J. Lederer and S. Van-de-geer, New concentration inequalities for suprema of empirical processes, Bernoulli, vol.20, issue.4, pp.2020-2038
DOI : 10.3150/13-BEJ549

M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM: Probability and Statistics, vol.1, pp.63-87, 1997.
DOI : 10.1051/ps:1997103

A. Marchina, Concentration inequalities for separately convex functions, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01344861

I. Pinelis, On a majorization inequality for sums of independent random vectors, Statistics & Probability Letters, vol.19, issue.2, pp.97-99, 1994.
DOI : 10.1016/0167-7152(94)90139-2

I. Pinelis, Optimum bounds for the distributions of martingales in banach spaces. The Annals of Probability, pp.1679-1706, 1994.

I. Pinelis, Optimal Tail Comparison Based on Comparison of Moments, High dimensional probability, pp.297-314, 1998.
DOI : 10.1007/978-3-0348-8829-5_19

I. Pinelis, Fractional sums and integrals of r-concave tails and applications to comparison probability inequalities Advances in stochastic inequalities, pp.149-168, 1997.

I. Pinelis, An Optimal Three-Way Stable and Monotonic Spectrum of Bounds on Quantiles: A Spectrum of Coherent Measures of Financial Risk and Economic Inequality, Risks, vol.72, issue.4, pp.349-392, 2014.
DOI : 10.1007/BF01311347

I. Pinelis, Convex cones of generalized multiply monotone functions and the dual cones, Banach Journal of Mathematical Analysis, vol.10, issue.4, pp.864-897
DOI : 10.1215/17358787-3649788

I. F. Pinelis and A. I. Sakhanenko, Remarks on Inequalities for Large Deviation Probabilities, Theory of Probability & Its Applications, vol.30, issue.1, pp.143-148, 1986.
DOI : 10.1137/1130013

E. Rio, Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions, Journal of Theoretical Probability, vol.5, issue.3, pp.146-163, 2009.
DOI : 10.1017/CBO9780511526237

URL : https://hal.archives-ouvertes.fr/hal-00679859

E. Rio, Asymptotic theory of weakly dependent random processes, volume 80 of Probability Theory and Stochastic Modelling

S. Van-de-geer and J. Lederer, The Bernstein-Orlicz norm and deviation inequalities. Probab. Theory Related Fields, pp.225-250, 2013.

A. W. Van-der-vaart and J. A. Wellner, Weak Convergence and Empirical Processes: With Applications to Statistics Springer Series in Statistics References References [1] R. Adamczak. A tail inequality for suprema of unbounded empirical processes with applications to Markov chains, Electron. J. Probab, vol.13, issue.34, pp.1000-1034, 1996.
DOI : 10.1007/978-1-4757-2545-2

C. Bennett and R. Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol.129, 1988.

V. Bentkus, An extension of the Hoeffding inequality to unbounded random variables, Lithuanian Mathematical Journal, vol.31, issue.4, pp.137-157, 2008.
DOI : 10.1214/EJP.v11-371

S. Boucheron, O. Bousquet, G. Lugosi, and P. Massart, Moment inequalities for functions of independent random variables, The Annals of Probability, vol.33, issue.2, pp.514-560, 2005.
DOI : 10.1214/009117904000000856

URL : https://hal.archives-ouvertes.fr/hal-00101850

S. Boucheron, G. Lugosi, and P. Massart, Concentration Inequalities: A Nonasymptotic Theory of Independence
DOI : 10.1093/acprof:oso/9780199535255.001.0001

URL : https://hal.archives-ouvertes.fr/hal-00794821

O. Bousquet, Concentration Inequalities for Sub-Additive Functions Using the Entropy Method, Stochastic inequalities and applications, pp.213-247, 2003.
DOI : 10.1007/978-3-0348-8069-5_14

F. Comte and C. Lacour, Anisotropic adaptive kernel deconvolution, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.49, issue.2
DOI : 10.1214/11-AIHP470

URL : https://hal.archives-ouvertes.fr/hal-00579608

. Ann and . Inst, Henri Poincaré Probab, Stat, vol.49, issue.2, pp.569-609, 2013.

B. Courbot, Rates of convergence in the functional CLT for martingales, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.328, issue.6, pp.509-513, 1999.
DOI : 10.1016/S0764-4442(99)80200-6

U. Einmahl and D. Li, Characterization of LIL behavior in Banach space, Transactions of the American Mathematical Society, vol.360, issue.12, pp.6677-6693, 2008.
DOI : 10.1090/S0002-9947-08-04522-4

T. Klein and E. Rio, Concentration around the mean for maxima of empirical processes, The Annals of Probability, vol.33, issue.3, pp.1060-1077, 2005.
DOI : 10.1214/009117905000000044

J. Lederer and S. Van-de-geer, New concentration inequalities for suprema of empirical processes, Bernoulli, vol.20, issue.4, pp.2020-2038
DOI : 10.3150/13-BEJ549

M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM: Probability and Statistics, vol.1, pp.63-87, 1997.
DOI : 10.1051/ps:1997103

URL : https://www.esaim-ps.org/10.1051/ps:1997103/pdf

A. Marchina, Concentration inequalities for suprema of unbounded empirical processes, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01545101

A. Marchina, Concentration inequalities for separately convex functions, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01344861

P. Massart, empirical processes, The Annals of Probability, vol.28, issue.2, pp.863-884, 2000.
DOI : 10.1214/aop/1019160263

V. V. Petrov, Limit Theorems of Probability Theory: Sequences of Independent Random Variables. Oxford science publications, 1995.

I. Pinelis, An Optimal Three-Way Stable and Monotonic Spectrum of Bounds on Quantiles: A Spectrum of Coherent Measures of Financial Risk and Economic Inequality, Risks, vol.72, issue.4, pp.349-392, 2014.
DOI : 10.1007/BF01311347

E. Rio, Une in??galit?? de Bennett pour les maxima de processus empiriquesA Bennet type inequality for maxima of empirical processes, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.38, issue.6, pp.1053-1057, 2002.
DOI : 10.1016/S0246-0203(02)01122-6

E. Rio, About the constants in the Fuk-Nagaev inequalities, Electronic Communications in Probability, vol.22, issue.0, p.12, 2017.
DOI : 10.1214/17-ECP57

S. Van-de-geer and J. Lederer, The Bernstein-Orlicz norm and deviation inequalities. Probab. Theory Related Fields, pp.225-250, 2013.

A. W. Van-der-vaart and J. A. Wellner, Weak Convergence and Empirical Processes: With Applications to Statistics, 1996.
DOI : 10.1007/978-1-4757-2545-2

A. W. Van-der-vaart and J. A. Wellner, A local maximal inequality under uniform entropy, Electronic Journal of Statistics, vol.5, issue.0, pp.192-2031709, 2011.
DOI : 10.1214/11-EJS605

G. Bennett, On the probability of large deviations from the expectation for sums of bounded, independent random variables, Biometrika, vol.50, issue.3-4, pp.528-535, 1963.
DOI : 10.1093/biomet/50.3-4.528

V. Bentkus, On Hoeffding?s inequalities, The Annals of Probability, vol.32, issue.2, pp.1650-1673, 2004.
DOI : 10.1214/009117904000000360

URL : http://doi.org/10.1214/009117904000000360

]. S. Bobkov, Localization proof of the Bakry?Ledoux isoperimetric inequality and some applications. Theory of Probability & Its Applications, pp.308-314, 2003.

S. Boucheron, G. Lugosi, and P. Massart, Concentration Inequalities: A Nonasymptotic Theory of Independence
DOI : 10.1093/acprof:oso/9780199535255.001.0001

URL : https://hal.archives-ouvertes.fr/hal-00794821

O. Bousquet, Concentration Inequalities for Sub-Additive Functions Using the Entropy Method, Stochastic inequalities and applications, pp.213-247, 2003.
DOI : 10.1007/978-3-0348-8069-5_14

P. , D. Moral, and E. Rio, Concentration inequalities for mean field particle models, Ann. Appl. Probab, vol.21, issue.3, pp.1017-1052, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00375134

A. Dembo and O. Zeitouni, Large deviations techniques and applications, volume 38 of Stochastic Modelling and Applied Probability, 1998.

W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1007/BF02883985

T. Klein, Une in??galit?? de concentration ?? gauche pour les processus empiriques, Comptes Rendus Mathematique, vol.334, issue.6, pp.501-504, 2002.
DOI : 10.1016/S1631-073X(02)02303-8

T. Klein and E. Rio, Concentration around the mean for maxima of empirical processes, The Annals of Probability, vol.33, issue.3, pp.1060-1077, 2005.
DOI : 10.1214/009117905000000044

M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM: Probability and Statistics, vol.1, pp.63-87, 1997.
DOI : 10.1051/ps:1997103

URL : https://www.esaim-ps.org/10.1051/ps:1997103/pdf

A. Marchina, Concentration inequalities for suprema of unbounded empirical processes, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01545101

P. Massart, empirical processes, The Annals of Probability, vol.28, issue.2, pp.863-884, 2000.
DOI : 10.1214/aop/1019160263

I. Pinelis, An Optimal Three-Way Stable and Monotonic Spectrum of Bounds on Quantiles: A Spectrum of Coherent Measures of Financial Risk and Economic Inequality, Risks, vol.72, issue.4, pp.349-392, 2014.
DOI : 10.1007/BF01311347

I. Pinelis, Convex cones of generalized multiply monotone functions and the dual cones, Banach Journal of Mathematical Analysis, vol.10, issue.4, pp.864-897
DOI : 10.1215/17358787-3649788

E. Rio, Inégalités de concentration pour les processus empiriques de classes de parties. Probab. Theory Related Fields, pp.163-175, 2001.
DOI : 10.1007/pl00008756

E. Rio, Une in??galit?? de Bennett pour les maxima de processus empiriquesA Bennet type inequality for maxima of empirical processes, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.38, issue.6, pp.1053-1057, 2002.
DOI : 10.1016/S0246-0203(02)01122-6

E. Rio, Sur la fonction de taux dans les in??galit??s de Talagrand pour les processus empiriques, Comptes Rendus Mathematique, vol.350, issue.5-6, pp.5-6303, 2012.
DOI : 10.1016/j.crma.2012.02.006

E. Rio, Asymptotic theory of weakly dependent random processes, volume 80 of Probability Theory and Stochastic Modelling

M. Sion, On general minimax theorems, Pacific Journal of Mathematics, vol.8, issue.1, pp.171-176, 1958.
DOI : 10.2140/pjm.1958.8.171

URL : http://msp.org/pjm/1958/8-1/pjm-v8-n1-p14-s.pdf

M. Talagrand, New concentration inequalities in product spaces, Inventiones Mathematicae, vol.126, issue.3, pp.505-563, 1996.
DOI : 10.1007/s002220050108

A. W. Van-der-vaart and J. A. Wellner, Weak Convergence and Empirical Processes: With Applications to Statistics, 1996.
DOI : 10.1007/978-1-4757-2545-2

L. Wu, Large Deviations, Moderate Deviations and LIL for Empirical Processes, The Annals of Probability, vol.22, issue.1, pp.17-271650, 1994.
DOI : 10.1214/aop/1176988846

URL : http://doi.org/10.1214/aop/1176988846

W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1007/BF02883985

A. Marchina, Concentration inequalities for suprema of unbounded empirical processes, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01545101

I. Pinelis, Optimal Tail Comparison Based on Comparison of Moments, High dimensional probability, pp.297-314, 1998.
DOI : 10.1007/978-3-0348-8829-5_19

I. Pinelis, Fractional sums and integrals of r-concave tails and applications to comparison probability inequalities Advances in stochastic inequalities, pp.149-168, 1997.

I. Pinelis, On the Bennett???Hoeffding inequality, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.50, issue.1, 2009.
DOI : 10.1214/12-AIHP495

I. Pinelis, On the Bennett???Hoeffding inequality, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.50, issue.1, pp.15-27
DOI : 10.1214/12-AIHP495

URL : http://doi.org/10.1214/12-aihp495

I. Pinelis, Convex cones of generalized multiply monotone functions and the dual cones, Banach Journal of Mathematical Analysis, vol.10, issue.4, pp.864-897
DOI : 10.1215/17358787-3649788

E. Rio, Inégalités de concentration pour les processus empiriques de classes de parties. Probab. Theory Related Fields, pp.163-175, 2001.
DOI : 10.1007/pl00008756

A. W. Van-der-vaart and J. A. Wellner, Weak Convergence and Empirical Processes: With Applications to Statistics References References, 1996.
DOI : 10.1007/978-1-4757-2545-2

S. Boucheron, G. Lugosi, and P. Massart, Concentration Inequalities: A Nonasymptotic Theory of Independence
DOI : 10.1093/acprof:oso/9780199535255.001.0001

URL : https://hal.archives-ouvertes.fr/hal-00794821

E. Rio, Inégalités exponentielles pour les processus empiriques Comptes Rendus de l'Académie des Sciences -Series I -Mathematics, pp.597-600, 2000.
DOI : 10.1016/s0764-4442(00)00210-x

E. Rio, Inégalités de concentration pour les processus empiriques de classes de parties. Probab. Theory Related Fields, pp.163-175, 2001.
DOI : 10.1007/pl00008756

E. Rio, Une in??galit?? de Bennett pour les maxima de processus empiriquesA Bennet type inequality for maxima of empirical processes, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.38, issue.6, pp.1053-1057, 2002.
DOI : 10.1016/S0246-0203(02)01122-6