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Book Review

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Book Information:

Author: Valentin V. Petrov
Title: Limit theorems of probability theory: Sequences of independent random variables
Additional book information: Oxford Studies in Probability, vol. 4, Oxford Science Publications, Clarendon Press, Oxford, 1995, ix + 292 pp., ISBN 0-19-853499-X, $90.00

References [Enhancements On Off] (What's this?)

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  • 2. V. Bentkus and F. Götze, On the lattice point problem for ellipsoids, Preprint 94-111 SFB 343, Universität Bielefeld, 1994, pp. 1-26.
  • 3. R.N. Bhattacharya and R. Ranga Rao, Normal Approximation and Asymptotic Expansions, Wiley, New York, 1976, Revised Reprint, Krieger, Malabar, Florida, 1986. MR 55:9219, MR 87k:60062
  • 4. E. Borel, Les probabilités denombrables et leur applications arithmétiques, Rend. Circ. Math. Palermo 27 (1909), 247-271.
  • 5. H. Cramér, Random Variables and Probablitiy Distributions, Cambridge Tracts, Cambridge University Press, Cambridge, England, 1937.
  • 6. M. D. Donsker, An Invariance Principle for Certain Probability Limit Theorems, Mem. Amer. Math. Soc. 6 (1951), 1-12. MR 12:723a
  • 7. J.L. Doob, Stochastic Processes, Wiley, New York, 1953. MR 15:445b
  • 8. E.B. Dynkin, Markov Processes, Volume 2, Springer-Verlag, Berlin, 1965. MR 33:1887
  • 9. A. Einstein, Investigations on the Theory of the Brownian Movement (R. Furth, ed.), Dover, New York, 1959. MR 17:1035g
  • 10. C. G. Esseen, Fourier Analysis of Distribution Functions. A Mathematical Study of the Laplace-Gaussian Law, Acta Math. 77 (1945), 1-125. MR 7:312a
  • 11. W. Feller, An Introduction to Probability Theory and Its Applications, Volume 2, Second Edition, Wiley, New York, 1971. MR 42:5292
  • 12. A. Friedman, Stochastic Differential Equations and Applications, Volume 1, Academic Press, New York, 1975. MR 58:13350a
  • 13. B.V. Gnedenko and A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, MA, 1954. MR 16:52d
  • 14. K. It$\hat {o}$, Lectures on Stochastic Processes, Tata Institute of Fundamental Research, Volume 24, Bombay, 1961.
  • 15. I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, 1988. MR 89c:60096
  • 16. A. Khinchine, Über einen Satz der Wahrscheinlichkeitsrechnung, Fund. Math. 6 (1924), 9-20.
  • 17. A.N. Kolmogorov, Über das Gesetz der iterierten Logarithmus, Math. Ann. 101 (1929), 126-135.
  • 18. P. Lévy, Théorie de l'Addition des Variables Alétoires, Gauthier-Villars, Paris, 1937.
  • 19. K.R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967. MR 37:2271
  • 20. V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975. MR 52:9335, MR 48:1288
  • 21. V. Strassen, An Invariance Principle for the Law of Iterated Logarithm, Z. Wahrsch. Verw. Geb. 3 (1964), 211-226. MR 30:5379
  • 22. N. Wiener, Differential Space, J. Math. Phys. 2 (1923), 131-174.

Review Information:

Reviewer: Rabi Bhattacharya
Affiliation: Indiana University
Journal: Bull. Amer. Math. Soc. 34 (1997), 85-88
MSC (1991): Primary 60F05, 60F10
DOI: https://doi.org/10.1090/S0273-0979-97-00700-3
Review copyright: © Copyright 1997 American Mathematical Society
American Mathematical Society