scholarly journals A remark on a large deviation theorem for Markov chain with a finite number of states

2005 ◽  
Vol 50 (3) ◽  
pp. 612-622 ◽  
Author(s):  
Zbigniew Szewczak ◽  
Zbigniew Szewczak
Keyword(s):  
Markov Chain ◽  
Finite Number ◽  
Large Deviation ◽  
Large Deviation Theorem

An asymptotic formula for the Bayes risk in discriminating between two Markov chains

2001 ◽  
Vol 38 (A) ◽  
pp. 131-141
Author(s):  
A. V. Nagaev
Keyword(s):  
Markov Chain ◽  
Asymptotic Formula ◽  
Markov Chains ◽  
Large Deviation ◽  
Bayes Risk ◽  
Absolutely Continuous ◽  
Sums Of Random Variables ◽  
Finite Dimensional ◽  
Large Deviation Theorem ◽  
The Common

The problem of discriminating between two Markov chains is considered. It is assumed that the common state space of the chains is finite and all the finite dimensional distributions are mutually absolutely continuous. The Bayes risk is expressed through large deviation probabilities for sums of random variables defined on an auxiliary Markov chain. The proofs are based on a large deviation theorem recently established by Z. Szewczak.

An asymptotic formula for the Bayes risk in discriminating between two Markov chains

2001 ◽  
Vol 38 (A) ◽  
pp. 131-141 ◽  
Author(s):  
A. V. Nagaev
Keyword(s):  
Markov Chain ◽  
Asymptotic Formula ◽  
Markov Chains ◽  
Large Deviation ◽  
Bayes Risk ◽  
Absolutely Continuous ◽  
Sums Of Random Variables ◽  
Finite Dimensional ◽  
Large Deviation Theorem ◽  
The Common

The problem of discriminating between two Markov chains is considered. It is assumed that the common state space of the chains is finite and all the finite dimensional distributions are mutually absolutely continuous. The Bayes risk is expressed through large deviation probabilities for sums of random variables defined on an auxiliary Markov chain. The proofs are based on a large deviation theorem recently established by Z. Szewczak.

The robustness of positive recurrence and recurrence of Markov chains under perturbations of the transition probabilities

1975 ◽  
Vol 12 (04) ◽  
pp. 744-752 ◽  
Author(s):  
Richard L. Tweedie
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Finite Number ◽  
Transition Probabilities ◽  
General State ◽  
Transition Matrices ◽  
Positive Recurrence ◽  
Markov Chain Models ◽  
Countable Space ◽  
General State Space

In many Markov chain models, the immediate characteristic of importance is the positive recurrence of the chain. In this note we investigate whether positivity, and also recurrence, are robust properties of Markov chains when the transition laws are perturbed. The chains we consider are on a fairly general state space : when specialised to a countable space, our results are essentially that, if the transition matrices of two irreducible chains coincide on all but a finite number of columns, then positivity of one implies positivity of both; whilst if they coincide on all but a finite number of rows and columns, recurrence of one implies recurrence of both. Examples are given to show that these results (and their general analogues) cannot in general be strengthened.

On the limiting distribution of the failure time of fibrous materials

1983 ◽  
Vol 15 (02) ◽  
pp. 331-348
Author(s):  
Wagner De Souza Borges
Keyword(s):  
Materials Science ◽  
Failure Time ◽  
Large Deviation ◽  
Limiting Distribution ◽  
Statistical Characteristics ◽  
Fibrous Materials ◽  
Large Deviation Theorem ◽  
Science Area ◽  
The Individual ◽  
Failure Time Distributions

A large deviation theorem of the Cramér–Petrov type and a ranking limit theorem of Loève are used to derive an approximation for the statisticaldistribution of the failure time of fibrous materials. For that, fibrousmaterials are modeled as a series of independent and identical bundles of parallel filaments and the asymptotic distribution of their failure time is determined in terms of statistical characteristics of the individual filaments, as both the number of filaments in each bundle and the number of bundles in the chain grow large simultaneously. While keeping the numbernof filaments in each bundle fixed and increasing only the chain lengthkleads to a Weibull limiting distribution for the failure time, letting both increase in such a way that logk(n)= o(n), we show that the limit distribution isfor. Since fibrous materials which are both long and have many filaments prevail, the result is of importance in the materials science area since refined approximations to failure-time distributions can be achieved.

Queues with semi-Markovian arrivals

1967 ◽  
Vol 4 (02) ◽  
pp. 365-379 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Finite Number ◽  
Waiting Time ◽  
Busy Period ◽  
Queueing System ◽  
Interarrival Time ◽  
Single Server ◽  
Queue Size

A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.

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