On Strong Versions of the Central Limit Theorem
β Scribed by Peter Schatte
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 305 KB
- Volume
- 137
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Multivariate variational inequalities are obtained in terms of the w-functions and the trace of a Fisher-type information matrix. In consequence of these inequalities, the multivariate central limit theorem arises in the sense of the total variation.
## Abstract Let {__S~n~__, __n__ β₯ 1} be partial sums of independent identically distributed random variables. The almost sure version of CLT is generalized on the case of randomly indexed sums {__S~Nn~__, __n__ β₯ 1}, where {__N~n~__, __n__ β₯ 1} is a sequence of positive integerβvalued random varia
## Abstract Stochastic geometry models based on a stationary Poisson point process of compact subsets of the Euclidean space are examined. Random measures on β^__d__^, derived from these processes using Hausdorff and projection measures are studied. The central limit theorem is formulated in a way
A unified martingale approach is presented for establishing the asymptotic normality of some sequences of random variables. It is applied to the numbers of inversions, rises, and peaks, respectively, as well as the oscillation and the sum of consecutive pair products of a random permutation.