Poisson limit theorem for countable Markov chains in Markovian environments

2003 ◽  
Vol 24 (3) ◽  
pp. 298-306
Author(s):  
Fang Da-fan ◽  
Wang Han-xing ◽  
Tang Mao-ning
Keyword(s):  
Limit Theorem ◽  
Markov Chains ◽  
Poisson Limit

Compound Poisson limit theorems for Markov chains

1997 ◽  
Vol 34 (1) ◽  
pp. 24-34 ◽  
Author(s):  
Shoou-Ren Hsiau
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Markov Chains ◽  
Limit Theorems ◽  
Compound Poisson ◽  
Poisson Limit

This paper establishes a compound Poisson limit theorem for the sum of a sequence of multi-state Markov chains. Our theorem generalizes an earlier one by Koopman for the two-state Markov chain. Moreover, a similar approach is used to derive a limit theorem for the sum of the k th-order two-state Markov chain.

Compound Poisson limit theorems for Markov chains

1997 ◽  
Vol 34 (01) ◽  
pp. 24-34
Author(s):  
Shoou-Ren Hsiau
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Markov Chains ◽  
Limit Theorems ◽  
Compound Poisson ◽  
Poisson Limit

This paper establishes a compound Poisson limit theorem for the sum of a sequence of multi-state Markov chains. Our theorem generalizes an earlier one by Koopman for the two-state Markov chain. Moreover, a similar approach is used to derive a limit theorem for the sum of the k th-order two-state Markov chain.

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

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