scholarly journals A Poisson limit theorem for a strongly ergodic non-homogeneous Markov chain

2003 ◽  
Vol 277 (2) ◽  
pp. 722-730 ◽  
Author(s):  
Han-xing Wang ◽  
Mao-ning Tang ◽  
Jian-chao Fang ◽  
Rong-ming Wang
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Homogeneous Markov Chain ◽  
Poisson Limit

scholarly journals The local limit theorem for sums of random variables defined on a homogeneous Markov chain in the case of the stable limit distribution law

1961 ◽  
Vol 1 (1-2) ◽  
pp. 7-16
Author(s):  
A. Aleškevičienė
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Limit Distribution ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Homogeneous Markov Chain ◽  
Stable Limit ◽  
Distribution Law ◽  
Sums Of Random Variables ◽  
Stable Limit Distribution

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: A. Алешкявичене. Локальная предельная теорема для сумм случайных величин, связанных в однородную цепь Маркова в случае устойчивого предельного распределения A. Aleškevičienė. Lokalinė ribinė teorema atsitiktinių dydžių, surištų homogenine Markovo grandine, sumoms stabilaus ribinio dėsnio atveju  

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.

Countable non-homogeneous Markov chains: asymptotic behaviour

1977 ◽  
Vol 9 (3) ◽  
pp. 542-552 ◽  
Author(s):  
Harry Cohn
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Asymptotic Behaviour ◽  
Transition Probabilities ◽  
Asymptotic Properties ◽  
Homogeneous Markov Chain ◽  
Homogeneous Case ◽  
Main Concept ◽  
State Classification ◽  
Ratio Limit

The paper deals with asymptotic properties of the transition probabilities of a countable non-homogeneous Markov chain, the main concept used in the proofs being that of the tail σ-field of the chain. A state classification similar to that existing in the homogeneous case is given and a strong ratio limit property is shown to parallel the basic limit theorem for positive homogeneous chains. Some global asymptotic properties for null chains are also derived.

VIII.—The Central Limit Theorem for a Convergent Non-homogeneous Finite Markov Chain

1959 ◽  
Vol 65 (2) ◽  
pp. 109-120
Author(s):  
J. L. Mott
Keyword(s):  
Markov Chain ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Stochastic Matrix ◽  
Homogeneous Markov Chain ◽  
Finite Markov Chain ◽  
The Central Limit Theorem

SynopsisThe distribution of xn, the number of occurrences of a given one of k possible states of a non-homogeneous Markov chain {Pj} in n successive trials, is considered. It is shown that if Pn → P, a positive-regular stochastic matrix, as n → ∞ then the distribution about its mean of xn/n½ tends to normality, and that the variance tends to that of the corresponding distribution associated with the homogeneous chain {P}.

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.

Countable non-homogeneous Markov chains: asymptotic behaviour

1977 ◽  
Vol 9 (03) ◽  
pp. 542-552 ◽  
Author(s):  
Harry Cohn
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Asymptotic Behaviour ◽  
Transition Probabilities ◽  
Asymptotic Properties ◽  
Homogeneous Markov Chain ◽  
Homogeneous Case ◽  
Main Concept ◽  
State Classification ◽  
Ratio Limit

The paper deals with asymptotic properties of the transition probabilities of a countable non-homogeneous Markov chain, the main concept used in the proofs being that of the tail σ-field of the chain. A state classification similar to that existing in the homogeneous case is given and a strong ratio limit property is shown to parallel the basic limit theorem for positive homogeneous chains. Some global asymptotic properties for null chains are also derived.

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.

Strong ergodicity for continuous-time, non-homogeneous Markov chains

1982 ◽  
Vol 19 (3) ◽  
pp. 692-694 ◽  
Author(s):  
Mark Scott ◽  
Barry C. Arnold ◽  
Dean L. Isaacson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Homogeneous Markov Chain ◽  
Strong Ergodicity

Characterizations of strong ergodicity for Markov chains using mean visit times have been found by several authors (Huang and Isaacson (1977), Isaacson and Arnold (1978)). In this paper a characterization of uniform strong ergodicity for a continuous-time non-homogeneous Markov chain is given. This extends the characterization, using mean visit times, that was given by Isaacson and Arnold.

Sign in / Sign up

Export Citation Format

Share Document