Markov chains /
Main Author: | |
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Format: | Book |
Language: | English |
Published: |
Cambridge, U.K. ; New York, NY, USA :
Cambridge University Press,
1997.
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Subjects: |
Table of Contents:
- 1. Discrete-time Markov chains. 1.1 Definition and basic properties.1.2 Class structure. 1.3 Hitting times and absorption probabilities.1.4 Strong Markov property. 1.5 Recurrence and transience. 1.6Recurrence and transience of random walks. 1.7 Invariant distributions.1.8 Convergence to equilibrium. 1.9 Time reversal. 1.10 Ergodictheorem. 1.11 Appendix: recurrence relations. 1.12 Appendix:asymptotics for n!
- 2. Continuous-time Markov chains I. 2.1Q-matrices and their exponentials. 2.2 Continuous-time randomprocesses. 2.3 Some properties of the exponential distribution. 2.4Poisson processes. 2.5 Birth processes. 2.6 Jump chain and holdingtimes. 2.7 Explosion. 2.8 Forward and backward equations. 2.9Non-minimal chains. 2.10 Appendix: matrix exponentials
- 3.Continuous-time Markov chains II. 3.1 Basic properties. 3.2 Classstructure. 3.3 Hitting times and absorption probabilities. 3.4Recurrence and transience. 3.5 Invariant distributions. 3.6 Convergenceto equilibrium. 3.7 Time reversal.