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Markov chains with stationary transition probabilities.

Author: Kai Lai Chung
Publisher: Berlin, New York, Springer, 1967.
Series: Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd. 104.
Edition/Format:   eBook : Document : English : 2d edView all editions and formats
Summary:
From the reviews: J. Neveu, 1962 in Zentralblatt fr Mathematik, 92. Band Heft 2, p. 343: "Ce livre crit par l'un des plus minents spcialistes en la matire, est un expos trs dtaill de la thorie des processus de Markov dfinis sur un espace dnombrable d'tats et homognes dans le temps (chaines stationnaires de Markov)." N. Jain, 2008 in Selected Works of Kai Lai Chung, edited by Farid AitSahlia (University of Florida,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Chung, Kai Lai, 1917-2009.
Markov chains with stationary transition probabilities.
Berlin, New York, Springer, 1967
(DLC) 66025793
(OCoLC)527777
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Kai Lai Chung
ISBN: 9783642620157 3642620159 9783642620171 3642620175
OCLC Number: 680108862
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Description: 1 online resource (x, 301 pages).
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: I. Discrete Parameter --
§ 1. Fundamental definitions --
§ 2. Transition probabilities --
§ 3. Classification of states --
§ 4. Recurrence --
§ 5. Criteria and examples --
§ 6. The main limit theorem --
§ 7. Various complements --
§ 8. Repetitive pattern and renewal process --
§ 9. Taboo probabilities --
§ 10. The generating function --
§ 11. The moments of first entrance time distributions --
§ 12. A random walk example --
§ 13. System theorems --
§ 14. Functionals and associated random variables --
§ 15. Ergodic theorems --
§ 16. Further limit theorems --
§ 17. Almost closed and sojourn sets --
II. Continuous Parameter --
§ 1. Transition matrix: basic properties --
§ 2. Standard transition matrix --
§ 3. Differentiability --
§ 4. Definitions and measure-theoretic foundations --
§ 5. The sets of constancy --
§ 6. Continuity properties of sample functions --
§ 7. Further specifications of the process --
§ 8. Optional random variable --
§ 9. Strong Markov property --
§ 10. Classification of states --
§ 11. Taboo probability functions --
§ 12. Last exit time --
§ 13. Ratio limit theorems; discrete approximations --
§ 14. Functionals --
§ 15. Post-exit process --
§ 16. Imbedded renewal process --
§ 17. The two systems of differential equations --
§ 18. The minimal solution --
§ 19. The first infinity --
§ 20. Examples.
Series Title: Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd. 104.

Abstract:

From the reviews: J. Neveu, 1962 in Zentralblatt fr Mathematik, 92. Band Heft 2, p. 343: "Ce livre crit par l'un des plus minents spcialistes en la matire, est un expos trs dtaill de la thorie des processus de Markov dfinis sur un espace dnombrable d'tats et homognes 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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