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Book Review
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Book Information
Author(s):
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.,
$90.00,
ISBN 0-19-853499-X
References:
- 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.
Additional Information:
Reviewer(s):
Rabi
Bhattacharya
Affiliation:
Indiana University
Review Information:
Journal:
Bull. Amer. Math. Soc.
34
(1997),
85-88.
MSC
(1991):
Primary 60F05, 60F10
DOI:
10.1090/S0273-0979-97-00700-3
PII:
S 0273-0979(97)00700-3
Copyright of article:
Copyright
1997,
American Mathematical Society
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