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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Official URL: http://sankhya.isical.ac.in/search/52a1/52a1005.ht...

## Abstract

The classical Poisson limit theorem studies the limit laws of S_{n} where S_{n}=∑ ^{n} _{j=1}X_{jn} and X_{1n},...,X_{nn} 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 (A_{n}(s))^{n} where s is a real parameter and A_{n}(s) is a finite dimensional (the dimension being fixed) matrix of the form A_{n}(s)=R(s)+n^{−1}(Q(s)+B_{n}(s)) where lim _{n→∞} B_{n}(s)=0. This problem seem to be of independent interest but does not appear to have been treated in the literature.

Item Type: | Article |
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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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