This volume is the second of three volumes devoted to the work of one of the most prominent twentieth-century mathematicians. Throughout his mathematical work, A.N. Kolmogorov (1903-1987) showed great creativity and versatility and his wide-ranging studies in many different areas led to the solution of conceptual and fundamental problems and the posing of new, important questions. His lasting contributions embrace probability theory and statistics, the theory of dynamical systems, mathematical logic, geometry and topology, the theory of functions and functional analysis, classical mechanics, the theory of turbulence, and information theory.
This second volume contains papers on probability theory and mathematical statistics, and embraces topics such as limit theorems, axiomatics and logical foundations of probability theory, Markov chains and processes, stationary processes and branching processes.
The material appearing in each volume was selected by A.N. Kolmogorov himself and is accompanied by short introductory notes and commentaries which reflect upon the influence of this work on the development of modern mathematics. All papers appear in English - some for the first time -- and in chronological order. This volume contains a significant legacy which will find many grateful beneficiaries amongst researchers and students of mathematics and mechanics, as well as historians of mathematics.
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: Mathematics and Its Applications : Book 2
Number Of Pages: 597
Published: 29th February 1992
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6
Weight (kg): 1.04