Markov set-chains / Darald J. Hartfiel

Auteur: Hartfiel, Darald J. (1939-) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1695Langue: anglaisÉditeur: Berlin : Springer, 1998 ISBN: 9783540647751 ISSN: 1617-9692Note: ... Chapter 1 covers the results on stochastic matrices which are used in the development of Markov chains, nonhomogeneous Markov chains, and Markov set-chains. Chapter 2 represents the basic part for the study of Markov set-chains that allow for fluctuating transition matrices at each step in time but yet providing a long run limit, and integrates the theory of classical Markov chains into a new setting. Chapter 3 investigates the conditions which assure a Markov set-chain (or related such chain) to converge, and describes the properties of the limit set. Chapter 4 shows how Markov set-chains are applied in the classical work of chain behaviour. The final Appendix gives a brief survey of several topics of mathematics used within this monograph: norms, operations on compact sets, convex sets and polytopes, probability theory results. Furthermore, each chapter includes illustrating examples and additional notes to the related results and literature. This useful monograph addresses a large area of mathematicians, engineers, economists, social and human scientists motivated by the development of interval techniques for the study of various systems that can show fluctuation. (Zentralblatt) Sujets MSC: 60J10 Probability theory and stochastic processes -- Markov processes -- Markov chains (discrete-time Markov processes on discrete state spaces)
52B55 Convex and discrete geometry -- Polytopes and polyhedra -- Computational aspects related to convexity
60-02 Probability theory and stochastic processes -- Research exposition (monographs, survey articles)
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... Chapter 1 covers the results on stochastic matrices which are used in the development of Markov chains, nonhomogeneous Markov chains, and Markov set-chains. Chapter 2 represents the basic part for the study of Markov set-chains that allow for fluctuating transition matrices at each step in time but yet providing a long run limit, and integrates the theory of classical Markov chains into a new setting. Chapter 3 investigates the conditions which assure a Markov set-chain (or related such chain) to converge, and describes the properties of the limit set. Chapter 4 shows how Markov set-chains are applied in the classical work of chain behaviour. The final Appendix gives a brief survey of several topics of mathematics used within this monograph: norms, operations on compact sets, convex sets and polytopes, probability theory results. Furthermore, each chapter includes illustrating examples and additional notes to the related results and literature. This useful monograph addresses a large area of mathematicians, engineers, economists, social and human scientists motivated by the development of interval techniques for the study of various systems that can show fluctuation. (Zentralblatt)

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