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This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.

Stochastic processes. --- Probabilities. --- Mathematical statistics. --- Dynamical systems. --- Stochastic Processes. --- Probability Theory. --- Mathematical Statistics. --- Applied Probability. --- Dynamical Systems. --- Stochastic Systems and Control. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Random processes --- Statistical methods --- Processos de Markov --- Sistemes de temps discret

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Bifurcation theory. --- System analysis. --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Differential equations, Nonlinear --- Stability --- Numerical solutions --- Teoria de la bifurcació --- Anàlisi de sistemes --- Cibernètica --- Física matemàtica --- Models matemàtics --- Teoria de sistemes --- Diagrames de flux --- Disseny de sistemes --- Identificació de sistemes --- Enginyeria de sistemes --- Mètodes de l'espai d'estat --- Sistemes borrosos --- Sistemes de temps discret --- Teoria de control --- Xarxes elèctriques --- Optimització matemàtica --- Teories no lineals --- Sistemes dinàmics diferenciables

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Discrete-time systems. --- Control theory. --- Iterative methods (Mathematics) --- Sistemes de temps discret --- Teoria de control --- Mètodes iteratius (Matemàtica) --- Iteration (Mathematics) --- Numerical analysis --- Dynamics --- Machine theory --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems --- Iteració (Matemàtica) --- Anàlisi numèrica --- Mètode de Newton-Raphson --- Control (Matemàtica) --- Control òptim --- Regulació --- Anàlisi de sistemes --- Teoria de màquines --- Control automàtic --- Filtre de Kalman --- Sistemes de control biològic --- Sistemes discrets --- Sistemes en temps discret --- Sistemes de control digital

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"The book covers up-to-date theoretical and applied advances in grey systems theory from across the world and vividly presents the reader with the overall picture of this new theory and its frontier research. Many of the concepts, models and methods in the book are original by the authors, including simplified form of grey number, general grey number and the operations of grey numbers; the axiomatic system of buffer operators and a series of weakening and strengthening operators; a series of grey relational analysis models, including grey absolute, relative, synthetic, similarity, closeness, negative and three dimension degree, etc.; grey fixed weight clustering model, grey evaluation models based on center-point and end-point mixed possibility functions; original difference grey model (ODGM), even difference grey model (EDGM), discrete grey model (DGM), fractional grey models, self-memory grey models; multi-attribute intelligent grey target decision models, weight vector group with kernel and the weighted comprehensive clustering coefficient vector, and spectrum analysis of sequence operators, etc. This book will be appropriate as a reference and/or professional book for courses of grey system theory for graduate students or high-level undergraduate students, majoring in areas of science, technology, agriculture, medicine, astronomy, earth science, economics, and management. It can also be utilized by researchers and practitioners in research institutions, business entities, and government agencies." -- Publisher's description.

System analysis. --- System analysis --- Anàlisi de sistemes --- Models matemàtics --- Mathematical models. --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Cibernètica --- Física matemàtica --- Teoria de sistemes --- Diagrames de flux --- Disseny de sistemes --- Identificació de sistemes --- Enginyeria de sistemes --- Mètodes de l'espai d'estat --- Sistemes borrosos --- Sistemes de temps discret --- Teoria de control --- Xarxes elèctriques --- Optimització matemàtica --- Teories no lineals --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Simulació per ordinador --- Teoria de màquines --- Models biològics

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Discrete-time systems --- Sistemes de temps discret --- Matemàtica --- Mathematics. --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems --- Matemàtiques (Ciència) --- Ciència --- Alfabetisme matemàtic --- Àlgebra --- Anàlisi matemàtica --- Aritmètica --- Axiomes --- Biomatemàtica --- Congruències (Geometria) --- Congruències i residus --- Constants matemàtiques --- Descomposició (Matemàtica) --- Dinàmica --- Estadística --- Factorització (Matemàtica) --- Filtres (Matemàtica) --- Formes (Matemàtica) --- Formes normals (Matemàtica) --- Geometria --- Geografia matemàtica --- Inducció (Matemàtica) --- Infinit --- Lògica matemàtica --- Matemàtica aplicada --- Matemàtica japonesa --- Màxims i mínims --- Nombres --- Quarta dimensió --- Successions (Matemàtica) --- Teoria de conjunts --- Teoria de l'índex (Matemàtica) --- Teoria de la computació --- Variables (Matemàtica) --- Didàctica de la matemàtica --- Ensenyament de la matemàtica --- Història de la matemàtica --- Matemàtics --- Sistemes discrets --- Sistemes en temps discret --- Anàlisi de sistemes --- Sistemes de control digital