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Volume 50

Number 5, October 1995

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COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY

1085
A minimal-degree polynomial for determining the volume of an octahedron from its metric

and

View article, A minimal-degree polynomial for determining the volume of an octahedron from its metric PDF, A minimal-degree polynomial for determining the volume of an octahedron from its metric
https://doi.org/10.1070/RM1995v050n05ABEH002620
1088
On a certain arithmetic function

View article, On a certain arithmetic function PDF, On a certain arithmetic function
https://doi.org/10.1070/RM1995v050n05ABEH002621
1090
On quadratic forms over the field

View article, On quadratic forms over the field PDF, On quadratic forms over the field
https://doi.org/10.1070/RM1995v050n05ABEH002623
1092
On the equation for the curvature of a curve changing in time and having a given distribution of distinguished points on it

and

View article, On the equation for the curvature of a curve changing in time and having a given distribution of distinguished points on it PDF, On the equation for the curvature of a curve changing in time and having a given distribution of distinguished points on it
https://doi.org/10.1070/RM1995v050n05ABEH002625
1095
On the gyrogroups of Hungar

View article, On the gyrogroups of Hungar PDF, On the gyrogroups of Hungar
https://doi.org/10.1070/RM1995v050n05ABEH002628
1097
The Krichever-Novikov algebras and CCC-groups

View article, The Krichever-Novikov algebras and CCC-groups PDF, The Krichever-Novikov algebras and CCC-groups
https://doi.org/10.1070/RM1995v050n05ABEH002630
849
The Khintchine inequalities and martingale expanding sphere of their action

and

View article, The Khintchine inequalities and martingale expanding sphere of their action PDF, The Khintchine inequalities and martingale expanding sphere of their action

Contents Introduction §1. The strong law of large numbers of Borel and its refinements §2. The Khintchine inequalities §3. Martingale extensions of the Khintchine inequalities. 1. Preliminary consideration §4. Martingale extensions of the Khintchine inequalities. 2. The Burkholder inequalities for §5. The maximal Khintchine inequalities §6. The martingale extension of maximal Khintchine inequalities. (The inequalities of Davis for and of Burkholder and Davis for ) §7. Comparison inequalities for martingale transforms §8. On the best constants in the Khintchine inequalities §9. The Khintchine inequalities in (exponential) Orlicz spaces §10. On the best constants in the Burkholder inequalities () §11. Some refinements of the Khintchine inequalities (the Whittle inequalities, the Rosenthal inequalities, and their modifications and extensions to the martingale case)

Bibliography

https://doi.org/10.1070/RM1995v050n05ABEH002594
905
Large deviations in power zones in the approximation by the Poisson law

and

View article, Large deviations in power zones in the approximation by the Poisson law PDF, Large deviations in power zones in the approximation by the Poisson law
https://doi.org/10.1070/RM1995v050n05ABEH002595
925
Rate of convergence in the functional law of the iterated logarithm with non-standard normalizing factors

and

View article, Rate of convergence in the functional law of the iterated logarithm with non-standard normalizing factors PDF, Rate of convergence in the functional law of the iterated logarithm with non-standard normalizing factors
https://doi.org/10.1070/RM1995v050n05ABEH002597
945
On normal approximation of a process with independent increments

View article, On normal approximation of a process with independent increments PDF, On normal approximation of a process with independent increments

Contents §1. Introduction §2. Proof of Theorem 1.1 §3. Some generalizations of the bound (1.2) §4. Examples §5. Poissonization of randomly indexed sums

Bibliography

https://doi.org/10.1070/RM1995v050n05ABEH002598
963
Statistical estimation of the entropy of discrete random variables with a large number of outcomes

and

View article, Statistical estimation of the entropy of discrete random variables with a large number of outcomes PDF, Statistical estimation of the entropy of discrete random variables with a large number of outcomes
https://doi.org/10.1070/RM1995v050n05ABEH002601
977
On large deviations for diffusion processes with measurable coefficients

View article, On large deviations for diffusion processes with measurable coefficients PDF, On large deviations for diffusion processes with measurable coefficients

Contents §1. Introduction §2. Main results §3. Proofs

Bibliography

https://doi.org/10.1070/RM1995v050n05ABEH002604
989
Large deviations for solutions of singularly perturbed stochastic differential equations

and

View article, Large deviations for solutions of singularly perturbed stochastic differential equations PDF, Large deviations for solutions of singularly perturbed stochastic differential equations

Contents §0. Introduction §1. Formulation of the main results §2. Exponential bounds in the uniform metric §3. Logarithmic asymptotics of the large deviation probability in the uniform metric §4. Logarithmic asymptotics of the deviation probability in the L2-metric §5. Moment bounds for linear equations

Bibliography

https://doi.org/10.1070/RM1995v050n05ABEH002607
1015
On a generalization of stable distributions

View article, On a generalization of stable distributions PDF, On a generalization of stable distributions
https://doi.org/10.1070/RM1995v050n05ABEH002611
1025
Three limit theorems for reduced critical branching processes

View article, Three limit theorems for reduced critical branching processes PDF, Three limit theorems for reduced critical branching processes

Contents §1. Introduction §2. Basic results §3. Discussion of Theorems 2.1-2.3 §4. The equation for the generating function §5. Equations for limit processes §6. Proof of the theorems §7. Proof of Lemmas 3.2 and 3.3

Bibliography

https://doi.org/10.1070/RM1995v050n05ABEH002613
1045
Asymptotic expansions of the probability that the sum of independent random variables hits a ball in a Hilbert space

and

View article, Asymptotic expansions of the probability that the sum of independent random variables hits a ball in a Hilbert space PDF, Asymptotic expansions of the probability that the sum of independent random variables hits a ball in a Hilbert space

Contents §1. Introduction and formulation of the main results §2. Auxiliary results §3. Proofs of the main results

Bibliography

https://doi.org/10.1070/RM1995v050n05ABEH002616
1065
On the correct extension of a problem of selecting the probability density under constraints on a system of mathematical expectations

View article, On the correct extension of a problem of selecting the probability density under constraints on a system of mathematical expectations PDF, On the correct extension of a problem of selecting the probability density under constraints on a system of mathematical expectations

Contents §1. Formulation of the elementary problem §2. Finitely additive measures §3. Admissible sets and their relaxation §4. Questions of asymptotic insensitivity of attainable sets §5. Extremal selection of a stepwise density function §6. Optimization of the scalar criterion §7. Conclusion

Bibliography

https://doi.org/10.1070/RM1995v050n05ABEH002618