منابع مشابه
Central Limit Theorems for Generalized Pólya Urn Models
In this paper we obtain central limit theorems for generalized Pólya urn models with L ≥ 2 colors where one out ofK different replacements (actions) is applied randomly at each step. Each possible action constitutes a row of the replacement matrix, which can be nonsquare and random. The actions are chosen following a probability distribution given by an arbitrary function of the proportions of ...
متن کاملCentral limit theorems for a hypergeometric randomly reinforced urn
We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number of extracted balls of a certain color given the past is assumed to be hypergeometric. We prove some central limit theorems in the sense of stable convergence ...
متن کاملLocal limit theorems for finite and infinite urn models
Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.
متن کاملCentral limit theorems for a class of irreducible multicolor urn models
We take a unified approach to central limit theorems for a class of irreducible urn models with constant replacement matrix. Depending on the eigenvalue, we consider appropriate linear combinations of the number of balls of different colors. Then under appropriate norming the multivariate distribution of the weak limits of these linear combinations is obtained and independence and dependence is...
متن کاملLimit Theorems for Random Triangular Urn Schemes
In this paper we study a generalized Pólya urn with balls of two colors and a random triangular replacement matrix. We extend some results of Janson (2004), (2005) to the case where the largest eigenvalue of the mean of the replacement matrix is not in the dominant class. Using some useful martingales and the embedding method introduced in Athreya and Karlin (1968), we describe the asymptotic c...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1996
ISSN: 0304-4149
DOI: 10.1016/s0304-4149(96)00094-4