Limit distributions of sums of random variables defined on a finite homogeneous Markov chain. II

1994 ◽  
Vol 34 (1) ◽  
pp. 78-87
Author(s):  
V. Kazakevičius
Keyword(s):  
Markov Chain ◽  
Random Variables ◽  
Homogeneous Markov Chain ◽  
Limit Distributions ◽  
Sums Of Random Variables ◽  
Finite Homogeneous Markov Chain

On sums of random variables defined on a two-state Markov chain

1970 ◽  
Vol 7 (3) ◽  
pp. 761-765 ◽  
Author(s):  
H. J. Helgert
Keyword(s):  
Markov Chain ◽  
Transition Probabilities ◽  
Random Variables ◽  
Homogeneous Markov Chain ◽  
Sums Of Random Variables ◽  
Image Position

Assume the sequence of random variables x0, x1, x2, ··· forms a two-state, homogeneous Markov chain with transition probabilities and initial probabilities

On sums of random variables defined on a two-state Markov chain

1970 ◽  
Vol 7 (03) ◽  
pp. 761-765 ◽  
Author(s):  
H. J. Helgert
Keyword(s):  
Markov Chain ◽  
Transition Probabilities ◽  
Random Variables ◽  
Homogeneous Markov Chain ◽  
Sums Of Random Variables ◽  
Image Position

Assume the sequence of random variables x 0, x 1, x 2, ··· forms a two-state, homogeneous Markov chain with transition probabilities and initial probabilities

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  

Sums and weighted sums of a gamma Markov sequence

1988 ◽  
Vol 25 (01) ◽  
pp. 204-209 ◽  
Author(s):  
Ravindra M. Phatarfod
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Random Variables ◽  
Laplace Transforms ◽  
Weighted Sums ◽  
Sums Of Random Variables ◽  
Markov Sequence

We derive the Laplace transforms of sums and weighted sums of random variables forming a Markov chain whose stationary distribution is gamma. Both seasonal and non-seasonal cases are considered. The results are applied to two problems in stochastic reservoir theory.

Absorption Probabilities for Sums of Random Variables Defined on a Finite Markov Chain

1962 ◽  
Vol 58 (2) ◽  
pp. 286-298 ◽  
Author(s):  
H. D. Miller
Keyword(s):  
Markov Chain ◽  
Asymptotic Expression ◽  
Random Variables ◽  
Partial Sums ◽  
Finite Markov Chain ◽  
Initial State ◽  
Main Result Theorem ◽  
Sums Of Random Variables ◽  
Result Theorem ◽  
Image Position

SummaryThis paper is essentially a continuation of the previous one (5) and the notation established therein will be freely repeated. The sequence {ξr} of random variables is defined on a positively regular finite Markov chain {kr} as in (5) and the partial sums and are considered. Let ζn be the first positive ζr and let πjk(y), the ‘ruin’ function or absorption probability, be defined by The main result (Theorem 1) is an asymptotic expression for πjk(y) for large y in the case when , the expectation of ξ1 being computed under the unique stationary distribution for k0, the initial state of the chain, and unconditional on k1.

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