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

Front Cover
A.N. Shiryayev
Springer Science & Business Media, Feb 29, 1992 - Mathematics - 597 pages
lEt moi •...• si j'avait so comment en revenir, One service mathematics has rendered the je n'y serais point alle:' human race. It has put common sense back Ju1e. Veme where it belongs, 01\ the topmost shelf next to the dUlty canister labelled 'discarded non- Tbe series is divergent; therefore we may be sense'. able to do something with it. Erie T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple reweiting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'tftre of this series.
 

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Contents

On convergence of series whose terms are determined by random events
1
On the law of large numbers
11
On a limit formula of A Khinchin
13
On sums of independent random variables
15
On the law of the iterated logarithm
32
On the law of large numbers
43
General measure theory and probability calculus
48
On the strong law of large numbers
60
A formula of Gauss in the method of least squares
303
Branching random processes
309
Computation of final probabilities for branching random processes
315
Statistical theory of oscillations with continuous spectrum
321
On sums of a random number of random terms
331
A local limit theorem for classical Markov chains
338
Solution of a probabilistic problem relating to the mechanism of bed formation
364
Unbiased estimators
369

On analytical methods in probability theory
62
The waiting problem
109
The method of the median in the theory of errors
115
A generalization of the LaplaceLyapunov Theorem
118
On the general form of a homogeneous stochastic process
121
On computing the mean Brownian area
128
On the empirical determination of a distribution law
139
On the limit theorems of probability theory
147
On the theory of continuous random processes
156
On the problem of the suitability of forecasting formulas found by statistical methods
169
Random motions
176
Deviations from Hardys formulas under partial isolation
179
On the theory of Markov chains
182
On the statistical theory of metal crystallization
188
Markov chains with a countable number of possible states
193
On the reversibility of the statistical laws of nature
209
Solution of a biological problem
216
On a new confirmation of Mendels laws
222
Stationary sequences in Hilbert space
228
Interpolation and extrapolation of stationary random sequences
272
On the logarithmic normal distribution of particle sizes under grinding
281
Justification of the method of least squares
285
On differentiability of transition probabilities of timehomogeneous Markov processes with a countable number of states
395
A generalization of Poissons formula for a sample from a finite set
404
Some recent work on limit theorems in probability theory
406
On A V Skorokhods convergence
419
Two uniform limit theorems for sums of independent terms
429
Random functions and limit theorems
442
On the properties of P Levys concentration functions
459
Transition of branching processes to diffusion processes and related genetic problems
466
On the classes n of Fortet and BlancLapierre
470
On conditions of strong mixing of a Gaussian stationary process
471
Random functions of several variables almost all realizations of which are periodic
478
An estimate of the parameters of a complex stationary Gaussian Markov process
479
On the approximation of distributions of sums of independent terms by infinitely divisible distributions
484
Estimators of spectral functions of random processes
505
On the logical foundations of probability theory
515
Comments
520
Branching processes Nos 25 32 33 46 B A Sevastyanov
538
Spectral representation of random processes Nos 47
551
Wald identities No 35 A A Novikov
567
The method of least squares Nos 30 31 M B Malyutov
583
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