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- Title
An improvement of convergence rate estimates in the Lyapunov theorem.
- Authors
Shevtsova, I. G.
- Abstract
The article discusses a study that aims to identify accurate formula for convergence rate estimates in the Lyapunov theorem distribution functions. The researcher uses Prawitz' smoothing inequality in such a way that the obtained bounds monotonically increase absolute constant distribution function. It further employs Berry-Esseen theorem or inequality to quantify the rate in which convergence of the distribution function normally takes place. Study reveals that using Prawitz' smoothing inequality or theorem improves convergence rate estimates.
- Subjects
STOCHASTIC convergence; LYAPUNOV functions; DISTRIBUTION (Probability theory); DIFFERENTIAL equations; PROBABILITY measures; NUMERICAL analysis; SMOOTHING (Numerical analysis); ACCELERATION of convergence in numerical analysis; DIFFERENTIAL operators
- Publication
Doklady Mathematics, 2010, Vol 82, Issue 3, p862
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562410060062