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A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service

Muthukrishnan Senthil Kumar (2011)

RAIRO - Operations Research

This paper concerns a discrete time Geo[X]/G/1 retrial queue with general retrial time in which all the arriving customers require first essential service with probability α 0 while only some of them demand one of other optional services: type − r (r = 1, 2, 3,...M) service with probability α r . The system state distribution, the orbit size and the system size distributions are obtained in terms of generating functions. The stochastic decomposition law holds for the proposed model. Performance measures...

A Donsker theorem to simulate one-dimensional processes with measurable coefficients

Pierre Étoré, Antoine Lejay (2007)

ESAIM: Probability and Statistics

In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurable coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these quantities by solving some suitable elliptic PDE problems.

A duality principle for stationary random sequences

K. Urbanik (2000)

Colloquium Mathematicum

The paper is devoted to the study of stationary random sequences. A concept of dual sequences is discussed. The main aim of the paper is to establish a relationship between the errors of linear least squares predictions for sequences and their duals.

A dynamical system in a Hilbert space with a weakly attractive nonstationary point

Ivo Vrkoč (1993)

Mathematica Bohemica

A differential equation is a Hilbert space with all solutions bounded but with so finite nontrivial invariant measure is constructed. In fact, it is shown that all solutions to this equation converge weakly to the origin, nonetheless, there is no stationary point. Moreover, so solution has a non-empty Ω -set.

A family of L 2-spaces associated to the jumps of a Markov process

Valentin Grecea (2011)

Open Mathematics

Given the (canonical) Markov process associated with a sufficiently general semigroup (P t), we establish a result concerning the uniform completeness of a family of L 2-spaces naturally associated with the jumps of the process. An application of this result is presented.

A family of stationary processes with infinite memory having the same p-marginals. Ergodic and spectral properties

M. Courbage, D. Hamdan (2001)

Colloquium Mathematicae

We construct a large family of ergodic non-Markovian processes with infinite memory having the same p-dimensional marginal laws of an arbitrary ergodic Markov chain or projection of Markov chains. Some of their spectral and mixing properties are given. We show that the Chapman-Kolmogorov equation for the ergodic transition matrix is generically satisfied by infinite memory processes.

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