Roberta Jungblut-Hessel, Brigitte Plateau, William J. Stewart, Bernard Ycart (2010)
RAIRO - Operations Research
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In this paper we present a method to perform fast simulation of large Markovian systems. This method is based on the use of three concepts: Markov chain uniformization, event-driven dynamics, and modularity. An application of urban traffic simulation is presented to illustrate the performance of our approach.
Marta Tyran-Kamińska (2002)
Annales Polonici Mathematici
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A generalization of the Poisson driven stochastic differential equation is considered. A sufficient condition for asymptotic stability of a discrete time-nonhomogeneous Markov process is proved.
Franco Giannessi (2010)
RAIRO - Operations Research
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A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski (2015)
Banach Center Publications
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In this paper we study finite state conditional Markov chains (CMCs). We give two examples of CMCs, one which admits intensity, and another one, which does not admit an intensity. We also give a sufficient condition under which a doubly stochastic Markov chain is a CMC. In addition we provide a method for construction of conditional Markov chains via change of measure.
Tuğrul Dayar, Jean-Michel Fourneau, Nihal Pekergin (2010)
RAIRO - Operations Research
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We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
Luo, Jiaowan (2006)
Journal of Applied Mathematics and Stochastic Analysis
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M. Tuba (1981)
Matematički Vesnik
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Franco Giannessi (2002)
RAIRO - Operations Research - Recherche Opérationnelle
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A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.
Henryk Gacki
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We present new sufficient conditions for the asymptotic stability of Markov operators acting on the space of signed measures. Our results are based on two principles. The first one is the LaSalle invariance principle used in the theory of dynamical systems. The second is related to the Kantorovich-Rubinstein theorems concerning the properties of probability metrics. These criteria are applied to stochastically perturbed dynamical systems, a Poisson driven stochastic differential equation...
Regina Hildenbrandt (2003)
Discussiones Mathematicae Probability and Statistics
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Several peculiarities of stochastic dynamic programming problems where random vectors are observed before the decision ismade at each stage are discussed in the first part of this paper. Surrogate problems are given for such problems with distance properties (for instance, transportation problems) in the second part.
Štěpán Klapka, Petr Mayer (2002)
Applications of Mathematics
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The paper concerns the possibilities for mathematical modelling of safety related systems (equipment oriented on safety). Some mathematical models have been required by the present European Standards for the railway transport. We are interested in the possibility of using Markov’s models to meet these Standards. In the text an example of using that method in the interlocking equipment life cycle is given. An efficient aggregation/disaggregation method for computing some characteristics...
J. Gani (1966-1967)
Publications mathématiques et informatique de Rennes
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Efraim Shmerling (2010)
Mathematica Bohemica
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Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by , where is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.