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Paper Information

Journal:   BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY   2008 , Volume 34 , Number 1; Page(s) 23 To 35.
 
Paper: 

CENTRAL AND LOCAL LIMIT THEOREMS IN MARKOV DEPENDENT RANDOM VARIABLES

 
 
Author(s):  RAHIMZADEH SANI A.*
 
* 
 
Abstract: 

We consider an irreducible and aperiodic Markov chain {kn}n=0 over the finite state space E = {1, . . . , p} with positive regular transition matrix P = {pij} and additive component {Un} such that {Sn} = {(kn , Un)} is also a Markov chain over the state space e1 = E × R We prove a central and a local limit theorem for this chain when the probability density functions of {Sn}, conditional on the first and the last states of {kn}n=0, exist.

 
Keyword(s): CENTRAL LIMIT THEOREM, LOCAL LIMIT THEOREM, MARKOV ADDITIVE PROCESS, MAXIMUM MODULUS EIGENVALUE
 
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