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Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains

J. Dedecker, S. Gouëzel, F. Merlevède (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider a large class of piecewise expanding maps T of [0, 1] with a neutral fixed point, and their associated Markov chains Yi whose transition kernel is the Perron–Frobenius operator of T with respect to the absolutely continuous invariant probability measure. We give a large class of unbounded functions f for which the partial sums of f○Ti satisfy both a central limit theorem and a bounded law of the iterated logarithm. For the same class, we prove that the partial sums of f(Yi) satisfy a...

Some applications of probability generating function based methods to statistical estimation

Manuel L. Esquível (2009)

Discussiones Mathematicae Probability and Statistics

After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure...

Some aspects of balking and reneging in finite buffer queues

Amit Choudhury, Pallabi Medhi (2011)

RAIRO - Operations Research

In this paper, a single server finite buffer Markovian queuing system is analyzed with the additional restriction that customers may balk as well as renege. Reneging considered in literature is usually of position independent type where the reneging rate is constant irrespective of the position of the customer in the system. However there are many real world situations where this assumption does not hold. This paper is an attempt to model balking with position dependent reneging. Explicit closed...

Some aspects of balking and reneging in finite buffer queues

Amit Choudhury, Pallabi Medhi (2011)

RAIRO - Operations Research

In this paper, a single server finite buffer Markovian queuing system is analyzed with the additional restriction that customers may balk as well as renege. Reneging considered in literature is usually of position independent type where the reneging rate is constant irrespective of the position of the customer in the system. However there are many real world situations where this assumption does not hold. This paper is an attempt to model balking with position dependent reneging. Explicit closed...

Some Borel measures associated with the generalized Collatz mapping

K. Matthews (1992)

Colloquium Mathematicae

This paper is a continuation of a recent paper [2], in which the authors studied some Markov matrices arising from a mapping T:ℤ → ℤ, which generalizes the famous 3x+1 mapping of Collatz. We extended T to a mapping of the polyadic numbers ℤ ^ and construct finitely many ergodic Borel measures on ℤ ^ which heuristically explain the limiting frequencies in congruence classes, observed for integer trajectories.

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