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On Bounds for the Characteristic Functions of Some Degenerate Multidimensional Distributions
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T. Shervashidze
Published/Copyright:
March 3, 2010
Abstract
We discuss an application of an inequality for the modulus of the characteristic function of a system of monomials in random variables to the convergence of the density of the corresponding system of the sample mixed moments. Also, we consider the behavior of constants in the inequality for the characteristic function of a trigonometric analogue of the above-mentioned system when the random variables are independent and uniformly distributed. Both inequalities were derived earlier by the author from a multidimensional analogue of Vinogradov's inequality for a trigonometric integral. As a byproduct the lower bound for the spectrum of 
is obtained, where ๐ด๐ is the matrix of coefficients of the first ๐ + 1 Chebyshev polynomials of first kind.
Key words and phrases:: Degenerate multidimensional distributions; bounds for characteristic functions; multidimensional analogue of Vinogradov's inequality; convergence of the density of a system of sample mixed moments; Chebyshev polynomials of first kind
Received: 2003-02-24
Published Online: 2010-03-03
Published in Print: 2003-June
ยฉ Heldermann Verlag
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Articles in the same Issue
- On ARU-Resolutions of Uniform Spaces
- On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups
- On the Uniform Convergence and ๐ฟ-Convergence of Double Fourier Series with Respect to the WalshโKaczmarz System
- Dynamic Programming and Mean-Variance Hedging in Discrete Time
- Extending Quasi-Invariant Measures by Using Subgroups of a Given Group
- Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems
- General ๐-Estimators in the Presence of Nuisance Parameters. Skew Projection Technique
- A Unified Characterization of ๐-Optimal and Minimal Entropy Martingale Measures by Semimartingale Backward Equations
- On the Existence of Continuous Modifications of Vector-Valued Random Fields
- Weak Convergence of a Dirichlet-Multinomial Process
- Time-Dependent Barrier Options and Boundary Crossing Probabilities
- On Separation Properties for Families of Probability Measures
- Oscillation Theorems of Nonlinear Difference Equations of Second Order
- On Bounds for the Characteristic Functions of Some Degenerate Multidimensional Distributions
- Estimates of Fourier Coefficients
- On Approximate Large Deviations for 1D Diffusion
