A characterization of Markov solutions for stochastic differential equations with jumps
Anne Estrade (1997)
Séminaire de probabilités de Strasbourg
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Anne Estrade (1997)
Séminaire de probabilités de Strasbourg
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Jolanta Kazak (2013)
Annales Polonici Mathematici
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Poisson driven stochastic differential equations on a separable Banach space are examined. Some sufficient conditions are given for the asymptotic stability of a Markov operator P corresponding to the change of distribution from jump to jump. We also give criteria for the continuous dependence of the invariant measure for P on the intensity of the Poisson process.
Gracinda Rita Guerreiro, João Tiago Mexia (2008)
Discussiones Mathematicae Probability and Statistics
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Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassifications. These populations will be divided into a finite number of sub-populations. Assuming that: a) entries, reclassifications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are...
Maria Jankiewicz, T. Rolski (1977)
Applicationes Mathematicae
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Fournier, Nicolas (2006)
Electronic Communications in Probability [electronic only]
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Kharlamov, B.V. (2005)
Zapiski Nauchnykh Seminarov POMI
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Maria Jankiewicz (1978)
Applicationes Mathematicae
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Adam Bobrowski (2008)
Banach Center Publications
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The subject of the paper is reciprocal influence of pure mathematics and applied sciences. We illustrate the idea by giving a review of mathematical results obtained recently, related to the model of stochastic gene expression due to Lipniacki et al. [38]. In this model, featuring mRNA and protein levels, and gene activity, the stochastic part of processes involved in gene expression is distinguished from the part that seems to be mostly deterministic, and the dynamics is expressed by...
J. Zabczyk (1985)
Banach Center Publications
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A. Plucińska (1971)
Applicationes Mathematicae
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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.
W. P. Cherry, R. L. Disney (1983)
Applicationes Mathematicae
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Michał Kisielewicz (2006)
Discussiones Mathematicae Probability and Statistics
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Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.
Piotr Nowak (2008)
Control and Cybernetics
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Friedrich Liese (1992)
Kybernetika
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A. Genadot, M. Thieullen (2014)
ESAIM: Probability and Statistics
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In [A. Genadot and M. Thieullen, Averaging for a fully coupled piecewise-deterministic markov process in infinite dimensions. 44 (2012) 749–773], the authors addressed the question of averaging for a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimensions. In the present paper, we carry on and complete this work by the mathematical analysis of the fluctuations of the slow-fast system around the averaged limit. A central limit theorem is derived and the associated...