Selected works of A. N. Kolmogovrov. Volume II, Probability theory and mathematical statistics

V. 1. Mathematics And Mechanics -- V. 2. Probability Theory And Mathematical Statistics -- V. 3. Information Theory And The Theory Of Algorithms. Edited By V.m. Tikhomirov ; Translated From The Russian By V.m. Volosov. Includes Bibliographical References. Title page From the publishers of the Russian edition A few words about A.N. Kolmogorov 1. On convergence of series whose terms are determined by random events (with A. Khinchin) 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 Hilbert 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. Lévy's concentration functions 46. Transition of branching processes to diffusion processes and related genetic problems 47. On the classes Φ^(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 A.N. Kolmogorov. On the papers on probability theory and mathematical statistics Analytical methods in probability theory (N°9) (A.D. Ventsel) Markov processes with a countable number of states (N°10) (B.A. Sevast'yanov) Homogeneous random processes (N°13) (V.M. Zolotarev) Homogeneous Markov processes (N°39) (A.A. Yushkevich) Branching processes (N°25,32,33,46) (B.A. Sevast'yanov) Stationary sequences (N°27) (Yu.A. Rozanov) Stationary processes (N°48) (V.A. Statulyavichus) Statistics of processes (N°50) (A.N. Shiryaev) Spectral theory of stationary processes (N°34) (A.M. Yaglom) Spectral representation of random processes (N°47,49) (Yu. G. Balasanov and I. G. Zhurbenko) Brownian motion (N°14,19,24) (A.M. Yaglom) Markov chains with a countable number of states (N°23) (A.A. Yushkevich) Wald identities (N°35) (A.A. Novikov) S-Convergence (N°42) (A. V. Skorokhod) Uniform limit theorems (N°43,51) (T. V. Arak) Concentration functions (N°45) (V.M. Kruglov) Empirical distributions (N°15) (E. V. Khmaladze) The method of least squares (N°30,31) (M.B. Malyutov) Unbiased estimators (N°38) (Yu.K. Belyaev and Ya.P. Lumel'skii) Statistical prediction (N°18) (A.M. Yaglom) On inter-bed washout (N°37) (A.B. Vistelius) 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 processes, stationary processes and branching processes.