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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,
$90.00$
Aloisio Araujo and Evarist Giné, The central limit theorem for real and Banach valued random variables, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York-Chichester-Brisbane, 1980. MR 576407
2. V. Bentkus and F. Götze, On the lattice point problem for ellipsoids, Preprint 94-111 SFB 343, Universität Bielefeld, 1994, pp. 1-26.
R. N. Bhattacharya and R. Ranga Rao, Normal approximation and asymptotic expansions, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York-London-Sydney, 1976. MR 0436272
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.
Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X
E. B. Dynkin, Markov processes. Vols. I, II, Die Grundlehren der mathematischen Wissenschaften, Band 121, vol. 122, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. Translated with the authorization and assistance of the author by J. Fabius, V. Greenberg, A. Maitra, G. Majone. MR 0193671
Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
P. Erdös and T. Grünwald, On polynomials with only real roots, Ann. of Math. (2) 40 (1939), 537–548. MR 7, DOI 10.2307/1968938
William Feller, An introduction to probability theory and its applications. Vol. II. , 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0270403
Avner Friedman, Stochastic differential equations and applications. Vol. 1, Probability and Mathematical Statistics, Vol. 28, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0494490
Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
14. K. It, Lectures on Stochastic Processes, Tata Institute of Fundamental Research, Volume 24, Bombay, 1961.
Ioannis Karatzas and Steven E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol. 113, Springer-Verlag, New York, 1988. MR 917065, DOI 10.1007/978-1-4684-0302-2
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.
K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MR 0226684
V. V. Petrov, Sums of independent random variables, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 82, Springer-Verlag, New York-Heidelberg, 1975. Translated from the Russian by A. A. Brown. MR 0388499
V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 211–226 (1964). MR 175194, DOI 10.1007/BF00534910
22. N. Wiener, Differential Space, J. Math. Phys. 2 (1923), 131-174.
- 1.
- A. Araujo and E. Giné, The Central Limit Theorem for Real and Banach Valued Random Variables, Wiley, New York, 1980. MR 83e:60003
- 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, 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
DOI:
https://doi.org/10.1090/S0273-0979-97-00700-3
Review copyright:
© Copyright 1997
American Mathematical Society