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Limit Theorems in Probability Theory

The following sources are recommended by a professor whose research specialty is probability.


Six Superlative Sources

· B.V. Knedenko and A.N. Kolmogorov. Limit Distributions for Sums of Indepedent Random Variables. Original in Russian, 1949. English translation by K.L. Chung: Addison-Wesley, 1954.

· P. Billingsley. Convergence of Probability Measures. Wiley, 1968.

· W.F. Stout. Almost Sure Convergence. Academic Press, 1974.

· I.A. Ibragimov and Y.V. Linnik. Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff, 1971.

· M. Ledoux and M. Talagrand. Probability in Banach Spaces. Springer-Verlag, 1991.

· R.M. Dudley. Uniform Central Limit Theorems. Cambridge University Press, 1999.

Other Excellent Sources

· P. Lévy. Théorie de l'Addition des Variables Aléatoires. Gautier-Villars, 1954. (In French).

· K.R. Parthasarathy. Probability Measures on Metric Spaces. Academic Press, 1967.

· J. Jacod and A.N. Shiryaev. Limit Theorems for Stochastic Processes. Springer-Verlag, 1987.

· A. van der Vaart and J. Wellner. Weak Convergence and Empirical Processes. Springer-Verlag, 1996.

· A. Dembo and O. Zeitouni. Large Deviation Techniques and Applications. Second edition, Springer-Verlag, 1998.

· V.H. de la Peña and E. Giné. Decoupling: From Dependence to Independence. Springer-Verlag, 1999.

· D.V. Voiculescu, K.J. Dykema, and A. Nica. Free Random Variables. CRM Monograph Series, vol. 1, American Mathematical Society, 1992.

· A. Araujo and E. Giné. The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, 1980.

· D. Pollard. Convergence of Stochastic Processes. Springer-Verlag, 1984.

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