A matrix limit theorem with applications to probability theory

Puri, Prem S. ; Robertson, James B. ; Sinha, Kalyan B. (1990) A matrix limit theorem with applications to probability theory Sankhya - Series A, 52 (1). pp. 58-83. ISSN 0581-572X

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The classical Poisson limit theorem studies the limit laws of Sn where Sn=∑ n j=1Xjn and X1n,...,Xnn is a sequence of {0, 1} valued, independent, identically distributed random variables. In this paper we will weaken the independence assumption and investigate the possible limit laws for certain types of dependent sequences. This leads us to the study of the limit of (An(s))n where s is a real parameter and An(s) is a finite dimensional (the dimension being fixed) matrix of the form An(s)=R(s)+n−1(Q(s)+Bn(s)) where lim n→∞ Bn(s)=0. This problem seem to be of independent interest but does not appear to have been treated in the literature.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Markov Chains; Finitary Processes; Linear Operators; Matrix Limit Theorem; Probability Limit Laws of Dependent Variables
ID Code:61310
Deposited On:14 Sep 2011 08:53
Last Modified:14 Sep 2011 08:53

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