Estimates of the approximation of weighted sums of conditionally independent random variables by the normal law

DOI10.1186/1029-242X-2013-320zbMath1286.60024OpenAlexW2146170186WikidataQ59299759 ScholiaQ59299759MaRDI QIDQ2437699

Emanuele Dolera

Publication date: 13 March 2014

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2013-320

zbMATH Keywords

central limit theoremcompletely monotone functionconditional independenceTaylor formulaBerry-Esseen inequalities

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items (2)

Proof of a McKean conjecture on the rate of convergence of Boltzmann-equation solutions ⋮ Characterization of weak convergence of probability-valued solutions of general one-dimensional kinetic equations

Cites Work

• Some estimates of the normal approximation for independent non-identically distributed random variables
• Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
• On the real accuracy of approximation in the central limit theorem
• Entropy production by block variable summation and central limit theorems
• Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics
• The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation
• Reaching the best possible rate of convergence to equilibrium for solutions of Kac's equation via central limit theorem
• De Finetti's theorem for Markov chains
• Fourier-based distances and Berry-Esseen like inequalities for smooth densities
• On mixtures of distributions of Markov chains.
• On the rate of convergence in the entropic central limit theorem
• Fisher information inequalities and the central limit theorem
• Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
• Central Limit Theorems for Interchangeable Processes

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