Geodesic
A Note on Bernstein's Bivariate Inequality
Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 371-375

Voir la notice de l'article provenant de la source Cambridge University Press

An upper bound for P[Σ Xi≥tσ, Σ Yi ≥ tσ], where (Xi, Yi ), i = 1, 2, ..., n are bounded independent random variables, was given by Mullen (1973). An improvement to the bound is possible without further assumptions. 
Mullen, K. A Note on Bernstein's Bivariate Inequality. Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 371-375. doi: 10.4153/CMB-1979-048-4
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[1] 1. Bennett, G., (1962), Probability Inequalities for the Sum of Independent Random Variables. J. Amer. Statist. Ass. 57, 33-45. Google Scholar

[2] 2. Bernstein, S., (1924), Sur une modification de l' inégalité de Tchebichef (In Russian, French Summary). Ann. Sci. Inst. Sew. Ukraine Sect. Math I. Google Scholar

[3] 3. Mullen, K., (1973), Bernstein's Inequality in the Bivariate Case. Can. Math. Bull 16, 83-86. Google Scholar

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