Exponential convergence for sequences of random variables
β Scribed by Jiaming Sun
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 274 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
β¦ Synopsis
Using the compactness in large deviation theory, this note describes a large deviation upper bound by a lower semicontinuous function. It then obtains a characterization for exponential convergence and discusses exponential convergence rates.
π SIMILAR VOLUMES
Under mild conditions, a Bernstein-Hoe ding-type inequality is established for covariance invariant positively associated random variables. A condition is given for almost sure convergence, and the associated rate of convergence is speciΓΏed in terms of the underlying covariance function.
Benford's law assigns the probability log 10 (1 + 1=d) for ΓΏnding a number starting with speciΓΏc signiΓΏcant digit d. We show that exponentially distributed numbers obey this law approximatively, i.e., within bounds of 0.03.