A strong limit theorem on gambling system for Bernoulli sequences is extended to the sequences of arbitrary discrete random variables by using the conditional probabilities. Furthermore, by allowing the selection function to take values in an interval, the conception of random selection is generaliz
On a local limit theorem in strong sense
β Scribed by N.G. Gamkrelidze
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 222 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, a straightforward extension of the classical local limit theorem is given. In particular, necessary and sufficient conditions for local limit theorem are presented in terms of function of smoothness.
π SIMILAR VOLUMES
Given a Gaussian distribution G in l 2 we construct l 2 -valued i.i.d. random variables X 1 ; X 2 ; : : : such that: absolutely continuous with respect to G, and the total variation |F n -G| 9 0. This contrasts to Prokhorov's (Dokl. Akad. Nauk SSSR (N.S) 83 (1952) 797) local limit theorem in R k .
The purpose of this paper is to present strong versions of the central limit theorem for independent nonidentically distributed random variables. Let S n , n ΒΏ 1, be the partial sums of independent random variables with zero means and ΓΏnite variances and let a(x) be a real function. We present su ci