Displaying similar documents to “Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme”

Survival probabilities for HIV infected patients through semi-Markov processes

Giovanni Masala, Giuseppina Cannas, Marco Micocci (2014)

Biometrical Letters

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In this paper we apply a parametric semi-Markov process to model the dynamic evolution of HIV-1 infected patients. The seriousness of the infection is rendered by the CD4+ T-lymphocyte counts. For this purpose we introduce the main features of nonhomogeneous semi-Markov models. After determining the transition probabilities and the waiting time distributions in each state of the disease, we solve the evolution equations of the process in order to estimate the interval transition probabilities....

Semi-Markov processes for reliability studies

Christiane Cocozza-Thivent, Michel Roussignol (2010)

ESAIM: Probability and Statistics

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We study the evolution of a multi-component system which is modeled by a semi-Markov process. We give formulas for the avaibility and the reliability of the system. In the r-positive case, we prove that the quasi-stationary probability on the working states is the normalised left eigenvector of some computable matrix and that the asymptotic failure rate is equal to the absolute value of the convergence parameter r.

The expected cumulative operational time for finite semi-Markov systems and estimation

Brahim Ouhbi, Ali Boudi, Mohamed Tkiouat (2007)

RAIRO - Operations Research

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In this paper we, firstly, present a recursive formula of the empirical estimator of the semi-Markov kernel. Then a non-parametric estimator of the expected cumulative operational time for semi-Markov systems is proposed. The asymptotic properties of this estimator, as the uniform strongly consistency and normality are given. As an illustration example, we give a numerical application.

Single-use reliability computation of a semi-Markovian system

Guglielmo D'Amico (2014)

Applications of Mathematics

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Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation...

General approximation method for the distribution of Markov processes conditioned not to be killed

Denis Villemonais (2014)

ESAIM: Probability and Statistics

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We consider a strong Markov process with killing and prove an approximation method for the distribution of the process conditioned not to be killed when it is observed. The method is based on a Fleming−Viot type particle system with rebirths, whose particles evolve as independent copies of the original strong Markov process and jump onto each others instead of being killed. Our only assumption is that the number of rebirths of the Fleming−Viot type system doesn’t explode in finite time...