Markov Chains
Springer Berlin (Verlag)
978-3-642-62017-1 (ISBN)
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."
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.
Erscheint lt. Verlag | 17.7.2012 |
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Reihe/Serie | Grundlehren der mathematischen Wissenschaften |
Zusatzinfo | XI, 301 p. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 480 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
Schlagworte | 60XX, 60J10 • Approximation • differential equation • Equation • Function • Markov • Markov Chain • markov chains • Markov Property • Mathematics • Moment • Parameter • Probabilities • Probability • Random Variable • Random Walk • Theorem • Variable |
ISBN-10 | 3-642-62017-5 / 3642620175 |
ISBN-13 | 978-3-642-62017-1 / 9783642620171 |
Zustand | Neuware |
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