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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, John Wiley & Sons, New York-London-Sydney, 1976. Wiley Series in Probability and Mathematical Statistics. MR 0436272
    R. N. Bhattacharya and R. Ranga Rao, Normal approximation and asymptotic expansions, Robert E. Krieger Publishing Co., Inc., Melbourne, FL, 1986. Reprint of the 1976 original. MR 855460
  • 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. Vols. I, II, Translated with the authorization and assistance of the author by J. Fabius, V. Greenberg, A. Maitra, G. Majone. Die Grundlehren der Mathematischen Wissenschaften, Bände 121, vol. 122, Academic Press Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. MR 0193671
  • 9. A. Einstein, Investigations on the Theory of the Brownian Movement (R. Furth, ed.), Dover, New York, 1959. MR 17:1035g
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  • 11. William Feller, An introduction to probability theory and its applications. Vol. II., Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0270403
  • 12. Avner Friedman, Stochastic differential equations and applications. Vol. 1, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Probability and Mathematical Statistics, Vol. 28. MR 0494490
    Avner Friedman, Stochastic differential equations and applications. Vol. 2, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Probability and Mathematical Statistics, Vol. 28. MR 0494491
  • 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. Ioannis Karatzas and Steven E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol. 113, Springer-Verlag, New York, 1988. MR 917065
  • 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, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MR 0226684
  • 20. V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York-Heidelberg, 1975. Translated from the Russian by A. A. Brown; Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 82. MR 0388499
    V. V. Petrov, \cyr Summy nezavisimykh sluchaĭnykh velichin., Izdat. “Nauka”, Moscow, 1972 (Russian). MR 0322927
  • 21. V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 211–226 (1964). MR 0175194, https://doi.org/10.1007/BF00534910
  • 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
DOI: https://doi.org/10.1090/S0273-0979-97-00700-3
Review copyright: © Copyright 1997 American Mathematical Society