Selected Works II

1. Deviations From Hardy’s Formulas Under Partial Isolation

   • A. N. Shiryayev

   Pages 179-181

2. On The Theory of Markov Chains

   • A. N. Shiryayev

   Pages 182-187

3. On The Statistical Theory of Metal Crystallization

   • A. N. Shiryayev

   Pages 188-192

4. Markov Chains with A Countable Number of Possible States

   • A. N. Shiryayev

   Pages 193-208

5. On The Reversibility of The Statistical Laws of Nature

   • A. N. Shiryayev

   Pages 209-215

6. Solution of A Biological Problem

   • A. N. Shiryayev

   Pages 216-221

7. On A New Confirmation of Mendel’s Laws

   • A. N. Shiryayev

   Pages 222-227

8. Stationary Sequences in Hubert Space

   • A. N. Shiryayev

   Pages 228-271

9. Interpolation and Extrapolation of Stationary Random Sequences

   • A. N. Shiryayev

   Pages 272-280

10. On The Logarithmic Normal Distribution of Particle Sizes Under Grinding

    • A. N. Shiryayev

    Pages 281-284

11. Justification of The Method of Least Squares

    • A. N. Shiryayev

    Pages 285-302

12. A Formula of Gauss in The Method Of Least Squares

    • A. A. Petrov, Yu. M. Smirnov

    Pages 303-308

13. Branching Random Processes

    • N. A. Dmitriev

    Pages 309-314

14. Computation of Final Probabilities for Branching Random Processes

    • B. A. Sevastyanov

    Pages 315-320

15. Statistical Theory of Oscillations with Continuous Spectrum

    • A. N. Shiryayev

    Pages 321-330

16. On Sums of A Random Number of Random Terms

    • Yu. V. Prokhorov

    Pages 331-337

17. A Local Limit Theorem for Classical Markov Chains

    • A. N. Shiryayev

    Pages 338-363

18. Solution of A Probabilistic Problem Relating To The Mechanism of Bed Formation

    • A. N. Shiryayev

    Pages 364-368

19. Unbiased Estimators

    • A. N. Shiryayev

    Pages 369-394

20. On Differentiability of Transition Probabilities of Time-Homogeneous Markov Processes with A Countable Number of States

    • A. N. Shiryayev

    Pages 395-403

The creative work of Andrei N. Kolmogorov is exceptionally wide-ranging. In his studies on trigonometric and orthogonal series, the theory of measure and inte­gral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in­ formation theory, he solved many conceptual and fundamental problems and posed new questions which gave rise to a great deal of further research. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of central results, with many applications to mechanics, geophysics, linguistics and biology, among other subjects. This edition includes Kolmogorov's most important papers on mathematics and the natural sciences. It does not include his philosophical and ped­agogical studies, his articles written for the "Bolshaya Sovetskaya Entsiklopediya", his papers on prosody and applications of mathematics or his publications on general questions. The material of this edition was selected and compiled by Kolmogorov himself.

The first volume consists of papers on mathematics and also on turbulence and classical mechanics. The second volume is devoted to probability theory and mathematical statistics. The focus of the third volume is on information theory and the theory of algorithms.

• Estimator
• Finite
• Identity
• Median
• Normal distribution
• Probability theory
• Random variable
• Topology
• Variable
• calculus
• geometry
• mathematical statistics
• mathematics
• measure theory
• theorem

Policies and ethics