Markov Chains with Stationary Transition ProbabilitiesFrom the reviews: J. Neveu, 1962 in Zentralblatt für Mathematik, 92.Band Heft 2, p. 343: "Ce livre écrit par l'un des plus éminents spécialistes en la matière, est un exposé très détaillé de la théorie des processus de Markov définis sur un espace dénombrable d'états et homogènes dans le temps (chaines stationnaires de Markov)." N.Jain, 2008 in Selected Works of Kai Lai Chung, edited by Farid AitSahlia (University of Florida, USA), Elton Hsu (Northwestern University, USA), & Ruth Williams (University of California-San Diego, USA), Chapter 1, p. 15: "This monograph deals with countable state Markov chains in both discrete time (Part I) and continuous time (Part II). [...] Much of Kai Lai's fundamental work in the field is included in this monograph. Here, for the first time, Kai Lai gave a systematic exposition of the subject which includes classification of states, ratio ergodic theorems, and limit theorems for functionals of the chain." |
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Contents
Discrete Parameter 1 Fundamental definitions | 1 |
Transition probabilities | 5 |
Classification of states | 12 |
Copyright | |
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Common terms and phrases
arbitrary assertion Baire function Borel field Borel measurable CHUNG closed set conditional probability consequently continuous parameter converges Corollary to Theorem defined definition denoted discrete parameter DOOB equal equation Example exists FATOU's lemma follows from Theorem formula FUBINI's theorem Furthermore given Hence i-interval iɛI implies independent infinite initial distribution instantaneous interval Laplace transforms left member limit theorem Markov chains Markov processes Markov property Math minimal state space nonnegative nonrecurrent notation null set obtain optional relative p₁ Plim positive class post-a process proof of Theorem proved Q-matrix random variables random walk real numbers recurrent class right member sample functions satisfying separability sequence stable standard transition matrix stochastic process strong Markov property subset substochastic transition matrix Suppose T₁ tɛT theory transition probabilities zero Σ Σ