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A necessary and sufficient criterion weaker than the Markoff's hypothesis for asymptotical stability of stochastic semigroups of Markov operators on (L)-spaces is proven.

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A fluid queueing system in which the fluid flow in to the buffer is regulated by the state of the background queueing process is considered. In this model, the arrival and service rates follow chain sequence rates and are controlled by an exponential timer. The buffer content distribution along with averages are found using continued fraction methodology. Numerical results are illustrated to analyze the trend of the average buffer content for the model under consideration. It is interesting to note that the stationary solution of a fluid queue driven by a queue with chain sequence rates does not exist in the absence of exponential timer.

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Abstract  

This note concerns the asymptotic behavior of a Markov process obtained from normalized products of independent and identically distributed random matrices. The weak convergence of this process is proved, as well as the law of large numbers and the central limit theorem.

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Summary First we give a construction of bridges derived from a general Markov process using only its transition densities. We give sufficient conditions for their existence and uniqueness (in law).  Then we prove that the law of the radial part of the bridge with endpoints zero derived from a special multidimensional Ornstein--Uhlenbeck process equals the law of the bridge with endpoints zero derived from the radial part of the same Ornstein--Uhlenbeck process.  We also construct bridges derived from general multidimensional Ornstein--Uhlenbeck processes.

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478 493 CARMONA, P., PETIT, F. and YOR, M., Beta-gamma random variables and intertwining relations between certain Markov processes, Rev. Mat. Iberoamericana 14 (1998), 311

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Ethier, S. and Kurtz, T. (1986): Markov Processes, Characterization and Convergence . John Wiley and Sons, New York. Markov Processes, Characterization and Convergence

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Kurtz, T. , Markov processes: Characterization and convergence. Wiley Series in Probability and Mathematical Statistics . 1986. Fujita, Takahiko , A random walk analogue of Lévy’s theorem. Studia Sci

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) 1981 Williams, D. , Diffusions, Markov processes, and martingales. Vol. 1 , John Wiley & Sons Ltd. (Chichester, 1979). Foundations

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, 1987. Théorie du potentiel associée â une résolvante. Théorie des processus de Markov. [Potential theory associated with a resolvent. Theory of Markov processes], Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], 1417

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