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Probability theory and mathematical statistics

Author: A N Kolmogorov; Alʹbert Nikolaevich Shiri︠a︡ev
Publisher: Dordrecht ; Boston : Kluwer Academic Publishers, ©1992.
Series: Mathematics and its applications (Kluwer Academic Publishers)., Soviet series ;, 26.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:

Contains papers on probability theory and mathematical statistics. This book features topics such as limit theorems, axiomatics and logical foundations of probability theory, Markov chains and  Read more...

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Document Type: Book
All Authors / Contributors: A N Kolmogorov; Alʹbert Nikolaevich Shiri︠a︡ev
ISBN: 902772797X 9789027727978
OCLC Number: 25049786
Notes: Translation of: Teorii︠a︡ veroi︠a︡tnosteĭ i matematicheskai︠a︡ statistika.
Description: xv, 597 p. : ill. ; 25 cm.
Contents: 1. On convergence of series whose terms are determined by random events.- 2. On the law of large numbers.- 3. On a limit formula of A. Khinchin.- 4. On sums of independent random variables.- 5. On the law of the iterated logarithm.- 6. On the law of large numbers.- 7. General measure theory and probability calculus.- 8. On the strong law of large numbers.- 9. On analytical methods in probability theory.- 10. The waiting problem.- 11. The method of the median in the theory of errors.- 12. A generalization of the Laplace-Lyapunov Theorem.- 13. On the general form of a homogeneous stochastic process.- 14. On computing the mean Brownian area.- 15. On the empirical determination of a distribution law.- 16. On the limit theorems of probability theory.- 17. On the theory of continuous random processes.- 18. On the problem of the suitability of forecasting formulas found by statistical methods.- 19. Random motions.- 20. Deviations from Hardy's formulas under partial isolation.- 21. On the theory of Markov chains.- 22. On the statistical theory of metal crystallization.- 23. Markov chains with a countable number of possible states.- 24. On the reversibility of the statistical laws of nature.- 25. Solution of a biological problem.- 26. On a new confirmation of Mendel's laws.- 27. Stationary sequences in Hubert space.- 28. Interpolation and extrapolation of stationary random sequences...- 29. On the logarithmic normal distribution of particle sizes under grinding.- 30. Justification of the method of least squares.- 31. A formula of Gauss in the method of least squares.- 32. Branching random processes.- 33. Computation of final probabilities for branching random processes..- 34. Statistical theory of oscillations with continuous spectrum.- 35. On sums of a random number of random terms.- 36. A local limit theorem for classical Markov chains.- 37. Solution of a probabilistic problem relating to the mechanism of bed formation.- 38. Unbiased estimators.- 39. On differentiability of transition probabilities of time-homogeneous Markov processes with a countable number of states.- 40. A generalization of Poisson' s formula for a sample from a finite set.- 41. Some recent work on limit theorems in probability theory.- 42. On A.V. Skorokhod's convergence.- 43. Two uniform limit theorems for sums of independent terms.- 44. Random functions and limit theorems.- 45. On the properties of P. Levy's concentration functions.- 46. Transition of branching processes to diffusion processes and related genetic problems.- 47. On the classes ?(n) of Fortet and Blanc-Lapierre.- 48. On conditions of strong mixing of a Gaussian stationary process.- 49. Random functions of several variables almost all realizations of which are periodic.- 50. An estimate of the parameters of a complex stationary Gaussian Markov process.- 51. On the approximation of distributions of sums of independent terms by infinitely divisible distributions.- 52. Estimators of spectral functions of random processes.- 53. On the logical foundations of probability theory.- Comments On the papers on probability theory and mathematical statistics.- Analytical methods in probability theory (No. 9).- Markov processes with a countable number of states (No. 10).- Homogeneous random processes (No. 13).- Homogeneous Markov processes (No. 39).- Branching processes (Nos. 25, 32, 33, 46).- Stationary sequences (No. 27).- Stationary processes (No. 48).- Statistics of processes (No. 50).- Spectral theory of stationary processes (No. 34).- Spectral representation of random processes (Nos. 47, 49).- Brownian motion (Nos. 14, 19, 24).- Markov chains with a countable number of states (No. 23).- Wald identities (No. 35).- S-Convergence (No. 42).- Uniform limit theorems (Nos. 43, 51).- Concentration functions (No. 45).- Empirical distributions (No. 15).- The method of least squares (Nos. 30, 31).- Unbiased estimators (No. 38).- Statistical prediction (No. 18).- On inter-bed washout (No. 37).
Series Title: Mathematics and its applications (Kluwer Academic Publishers)., Soviet series ;, 26.
Other Titles: Teorii︠a︡ veroi︠a︡tnosteĭ i matematicheskai︠a︡ statistika.
Responsibility: edited by A.N. Shiryayev ; translated from the Russian by G. Lindquist.
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