Averaging and stability of quasilinear functional differential equations with Markov parameters.
Katafygiotis, Lambros, Tsarkov, Yevgeny (1999)
Journal of Applied Mathematics and Stochastic Analysis
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Katafygiotis, Lambros, Tsarkov, Yevgeny (1999)
Journal of Applied Mathematics and Stochastic Analysis
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Kateřina Helisová, Jakub Staněk (2016)
Applications of Mathematics
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The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived. Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison...
Joanna Kubieniec (2016)
Annales Mathematicae Silesianae
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In paper [4] there are considered random dynamical systems with randomly chosen jumps acting on Polish spaces. The intensity of this process is a constant λ. In this paper we formulate criteria for the existence of an invariant measure and asymptotic stability for these systems in the case when λ is not constant but a Lipschitz function.
Andrzej Lasota, James A. Yorke (1986)
Časopis pro pěstování matematiky
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Wiojciech Wajda (1991)
Applicationes Mathematicae
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Rozonoer, L.I. (1998)
Mathematical Problems in Engineering
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Katarzyna Horbacz
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We consider random dynamical systems with randomly chosen jumps on Polish spaces. They generalize Markov processes corresponding to iterated function systems, Poisson driven stochastic differential equations, and irreducible Markov systems. We formulate criteria for the existence of an invariant measure and asymptotic stability for these systems. Estimates of the lower pointwise and concentration dimension of invariant measures are also given.
David Nualart Rodón, M. Sanz (1979)
Stochastica
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This paper deals with the relationship between two-dimensional parameter Gaussian random fields verifying a particular Markov property and the solutions of stochastic differential equations. In the non Gaussian case some diffusion conditions are introduced, obtaining a backward equation for the evolution of transition probability functions.
Keepler, M. (1998)
Portugaliae Mathematica
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Dawid Czapla (2012)
Annales Polonici Mathematici
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Stettner [Bull. Polish Acad. Sci. Math. 42 (1994)] considered the asymptotic stability of Markov-Feller chains, provided the sequence of transition probabilities of the chain converges to an invariant probability measure in the weak sense and converges uniformly with respect to the initial state variable on compact sets. We extend those results to the setting of Polish spaces and relax the original assumptions. Finally, we present a class of Markov-Feller chains with a linear state space...
Manstavičius, Martynas (2005)
Electronic Communications in Probability [electronic only]
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T. Komorowski (1992)
Annales de l'I.H.P. Probabilités et statistiques
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