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AuthorChung, Kai Lai. author
TitleMarkov Chains [electronic resource] : With Stationary Transition Probabilities / by Kai Lai Chung
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1967
Edition Second Edition
Connect tohttp://dx.doi.org/10.1007/978-3-642-62015-7
Descript XI, 301 p. online resource

CONTENT

I. Discrete Parameter -- ยง 1. Fundamental definitions -- ยง 2. Transition probabilities -- ยง 3. Classification of states -- ยง 4. Recurrence -- ยง 5. Criteria and examples -- ยง 6. The main limit theorem -- ยง 7. Various complements -- ยง 8. Repetitive pattern and renewal process -- ยง 9. Taboo probabilities -- ยง 10. The generating function -- ยง 11. The moments of first entrance time distributions -- ยง 12. A random walk example -- ยง 13. System theorems -- ยง 14. Functionals and associated random variables -- ยง 15. Ergodic theorems -- ยง 16. Further limit theorems -- ยง 17. Almost closed and sojourn sets -- II. Continuous Parameter -- ยง 1. Transition matrix: basic properties -- ยง 2. Standard transition matrix -- ยง 3. Differentiability -- ยง 4. Definitions and measure-theoretic foundations -- ยง 5. The sets of constancy -- ยง 6. Continuity properties of sample functions -- ยง 7. Further specifications of the process -- ยง 8. Optional random variable -- ยง 9. Strong Markov property -- ยง 10. Classification of states -- ยง 11. Taboo probability functions -- ยง 12. Last exit time -- ยง 13. Ratio limit theorems; discrete approximations -- ยง 14. Functionals -- ยง 15. Post-exit process -- ยง 16. Imbedded renewal process -- ยง 17. The two systems of differential equations -- ยง 18. The minimal solution -- ยง 19. The first infinity -- ยง 20. Examples


Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes



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