Selected Works of A.N. Kolmogorov. Volume II: Probability Theory and Mathematical Statistics

Front Matter....Pages i-xv
On Convergence of Series Whose Terms are Determined by Random Events....Pages 1-10
On The Law of Large Numbers....Pages 11-12
On A Limit Formula of A. Khinchin....Pages 13-14
On Sums of Independent Random Variables....Pages 15-31
On The Law of The Iterated Logarithm....Pages 32-42
On The Law of Large Numbers....Pages 43-47
7. General Measure Theory and Probability Calculus....Pages 48-59
On The Strong Law of Large Numbers....Pages 60-61
On Analytical Methods In Probability Theory....Pages 62-108
The Waiting Problem....Pages 109-114
The Method of The Median in The Theory of Errors....Pages 115-117
A Generalization of The Laplace-Lyapunov Theorem....Pages 118-120
On The General Form of A Homogeneous Stochastic Process....Pages 121-127
On Computing The Mean Brownian Area....Pages 128-138
15. On The Empirical Determination of A Distribution Law....Pages 139-146
On The Limit Theorems of Probability Theory....Pages 147-155
On The Theory of Continuous Random Processes....Pages 156-168
On The Problem of The Suitability of Forecasting Formulas Found by Statistical Methods....Pages 169-175
Random Motions....Pages 176-178
Deviations From Hardy’s Formulas Under Partial Isolation....Pages 179-181
On The Theory of Markov Chains....Pages 182-187
On The Statistical Theory of Metal Crystallization....Pages 188-192
Markov Chains with A Countable Number of Possible States....Pages 193-208
On The Reversibility of The Statistical Laws of Nature....Pages 209-215
Solution of A Biological Problem....Pages 216-221
On A New Confirmation of Mendel’s Laws....Pages 222-227
Stationary Sequences in Hubert Space....Pages 228-271
Interpolation and Extrapolation of Stationary Random Sequences....Pages 272-280
On The Logarithmic Normal Distribution of Particle Sizes Under Grinding....Pages 281-284
Justification of The Method of Least Squares....Pages 285-302
A Formula of Gauss in The Method Of Least Squares....Pages 303-308
Branching Random Processes....Pages 309-314
Computation of Final Probabilities for Branching Random Processes....Pages 315-320
Statistical Theory of Oscillations with Continuous Spectrum....Pages 321-330
On Sums of A Random Number of Random Terms....Pages 331-337
A Local Limit Theorem for Classical Markov Chains....Pages 338-363
Solution of A Probabilistic Problem Relating To The Mechanism of Bed Formation....Pages 364-368
Unbiased Estimators....Pages 369-394
On Differentiability of Transition Probabilities of Time-Homogeneous Markov Processes with A Countable Number of States....Pages 395-403
A Generalization of Poisson’s Formula for A Sample From A Finite Set....Pages 404-405
Some Recent Work on Limit Theorems in Probability Theory....Pages 406-418
On A.V. Skorokhod’s Convergence....Pages 419-428
Two Uniform Limit Theorems for Sums of Independent Terms....Pages 429-441
Random Functions and Limit Theorems....Pages 442-458
On The Properties of P. Levy’s Concentration Functions....Pages 459-465
Transition of Branching Processes to Diffusion Processes and Related Genetic Problems....Pages 466-469
On The Classes φ( n ) of Fortet and Blanc-Lapierre....Pages 470-470
On Conditions of Strong Mixing of A Gaussian Stationary Process....Pages 471-477
Random Functions of Several Variables Almost All Realizations of Which are Periodic....Pages 478-478
An Estimate of The Parameters of A Complex Stationary Gaussian Markov Process....Pages 479-483
On The Approximation of Distributions of Sums of Independent Terms by Infinitely Divisible Distributions....Pages 484-504
Estimators of Spectral Functions of Random Processes....Pages 505-514
On The Logical Foundations of Probability Theory....Pages 515-519
Comments....Pages 520-522
Analytical Methods in Probability Theory (No. 9)....Pages 522-527
Markov Processes with A Countable Number of States (No. 10)....Pages 528-528
Homogeneous Random Processes (No. 13)....Pages 528-530
Homogeneous Markov Processes (No. 39)....Pages 530-537
Branching Processes (Nos. 25, 32, 33, 46)....Pages 538-539
Stationary Sequences (No. 27)....Pages 539-542
Stationary Processes (No. 48)....Pages 542-544
Statistics of Processes (No. 50)....Pages 544-544
Spectral Theory of Stationary Processes (No. 34)....Pages 545-551
Spectral Representation of Random Processes (Nos. 47, 49)....Pages 551-554
Brownian Motion (Nos. 14, 19, 24)....Pages 554-559
Markov Chains with A Countable Number of States (No. 23)....Pages 559-566
Wald Identities (No. 35)....Pages 567-569
 S -Convergence (No. 42)....Pages 569-570
Uniform Limit Theorems (Nos. 43, 51)....Pages 570-571
Concentration Functions (No. 45)....Pages 571-574
Empirical Distributions (No. 15)....Pages 574-583
The Method of Least Squares (Nos. 30, 31)....Pages 583-584
Unbiased Estimators (No. 38)....Pages 585-587
Statistical Prediction (No. 18)....Pages 587-591
On Inter-Bed Washout (No. 37)....Pages 591-597