Buch, Englisch, 440 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 1079 g
Theory and Applications
Buch, Englisch, 440 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 1079 g
ISBN: 978-1-138-03452-5
Verlag: Chapman and Hall/CRC
Non-Homogeneous Markov Chains and Systems: Theory and Applications fulfills two principal goals. It is devoted to the study of non-homogeneous Markov chains in the first part, and to the evolution of the theory and applications of non-homogeneous Markov systems (populations) in the second. The book is self-contained, requiring a moderate background in basic probability theory and linear algebra, common to most undergraduate programs in mathematics, statistics, and applied probability. There are some advanced parts, which need measure theory and other advanced mathematics, but the readers are alerted to these so they may focus on the basic results.
Features
- A broad and accessible overview of non-homogeneous Markov chains and systems
- Fills a significant gap in the current literature
- A good balance of theory and applications, with advanced mathematical details separated from the main results
- Many illustrative examples of potential applications from a variety of fields
- Suitable for use as a course text for postgraduate students of applied probability, or for self-study
- Potential applications included could lead to other quantitative areas
The book is primarily aimed at postgraduate students, researchers, and practitioners in applied probability and statistics, and the presentation has been planned and structured in a way to provide flexibility in topic selection so that the text can be adapted to meet the demands of different course outlines. The text could be used to teach a course to students studying applied probability at a postgraduate level or for self-study. It includes many illustrative examples of potential applications, in order to be useful to researchers from a variety of fields.
Autoren/Hrsg.
Weitere Infos & Material
1. Foundations of Probability Theory. 1.1. Introductory Notes. 1.2. Some set theory and topology. 1.3. Important family of Sets in Probability theory. 1.4. Measurable spaces. 1.5. Probability spaces. 1.6. Filtration. 1.7. Random Variables. 1.8. Integration with respect to a probability measure. Expectation of a random variable. 1.9. Indicator functions. 1.10. The space L2 is a Hilbert space. 1.11. Independent s-algebras and random variables. 1.12. Convergence of sequences of random variables. 1.13. The Laws of Large Numbers and the Central Limit Theorem. 1.14. Conditional Distributions and Conditional Expectations. 1.15. Change of measure. 1.16. Existence and Uniqueness of Conditional Expectations. 1.17. Properties of Conditional Expectation. 2. A Small Review of Matrix Analysis. 2.1. Introductory Notes. 2.2. Matrices. 2.3. The minimal polynomial of A. 2.4. The Norm of a vector. 2.5. The matrix norm. 2.6. The Kronecker product of two matrices. 2.7. The Hadamard product of matrices. 2.8. Canonical forms of a matrix. 2.9. Generalized Inverses. 2.10. The Moore-Penrose Generalized Matrix. 2.11. The Drazin Inverse and the Group Inverse. 2.12. The Group Inverse and Markov Chains. 2.13. Sensitivity of Markov Chains. 3. Non-Homogeneous Markov Chains, Weak Ergodicity. 3.1. Introductory notes. 3.2. Stochastic processes. 3.3. Markov chain. 3.4. The life and work of A.A. Markov. 3.5. Probability distribution in the states of a nonhomogeneous Markov chain. 3.6. Examples. 3.7. Weak and Strong Ergodicity. 3.8. Structures for coefficients of ergodicity. 3.9. Conditions for weak ergodicity for general products of stochastic matrices. 3.10. The dominant role of the Dobrushin ergodicity coefficient. 3.11. Transition probability matrices are in chronological order. 3.12. Examples on the use of weak ergodicity theorems. 4. Non-Homogeneous Markov Chains, Strong Ergodicity. 4.1. Strong Ergodicity. 4.2. Characterization of ergodicity and geometric strong e
