Theorems of large deviations for sums of random variables connected in a Markov chain. II

1999 ◽  
Vol 39 (1) ◽  
pp. 64-85
Author(s):  
K. Padvelskis ◽  
V. Statulevičius
Keyword(s):  
Markov Chain ◽  
Large Deviations ◽  
Random Variables ◽  
Sums Of Random Variables

scholarly journals Asymptotic expansions for the probabilities of large deviations for sums of random variables related to a Markov chain

1970 ◽  
Vol 10 (2) ◽  
pp. 359-366
Author(s):  
L. Saulis ◽  
V. Statulevičius
Keyword(s):  
Markov Chain ◽  
Large Deviations ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Sums Of Random Variables ◽  
Probabilities Of Large Deviations

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: Л. И. Саулис, В. А. Статулявичус. Асимптотическое разложение для вероятностей больших уклонений сумм случайных величин, связанных в цепь Маркова L. Saulis, V. Statulevičius. Atsitiktinių dydžių, surištų į Markovo grandinę, didžiųjų nukrypimų asimptotinis dėstinys

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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