منابع مشابه
The Local Limit Theorem: A Historical Perspective
The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...
متن کاملOn a Bound for the Rate of Convergence in the Multidimensional Central Limit Theorem
In recent years many papers concerned with estimation of the rate of convergence in the central limit theorem in Rk have appeared (see [1], [2], [6]-[8], [10], [13]-[16]). They have significantly extended our knowledge in this area. We shall mention here two recent results which are most closely related to the estimate obtained in the present paper. V. Rotar [14], applying the method of charact...
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Abstract: Let n particles be independently allocated into N boxes, where the l-th box appears with the probability al. Let μr be the number of boxes with exactly r particles and μ = [μr1 , . . . , μrm ]. Asymptotical behavior of such random variables as N tends to infinity was studied by many authors. It was previously known that ifNal are all upper bounded and n/N is upper and lower bounded by...
متن کاملA Multivariate Central Limit Theorem for Continuous Local Martingales
A theorem on the weak convergence of a properly normalized multivariate continuous local martingale is proved. The time-change theorem used for this purpose allows for short and transparent arguments. 1991 Mathematics Subject Classification: 60F05, 60G44
متن کاملThe Local Central Limit Theorem for a Gibbs Random Field
We extend the validity of the implication of a local limit theorem from an integral one. Our extension eliminates the finite range assumption present in the previous works by using the cluster expansion to analyze the contribution from the tail of the potential. 1. Definitions and Results 1.1. Assumptions We consider a v-dimensional lattice spin system, to each χeZ is associated a spin sx that ...
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ژورنال
عنوان ژورنال: Lithuanian Mathematical Journal
سال: 1964
ISSN: 2669-1973
DOI: 10.15388/lmj.1964.19485