| Description |
1 online resource (473 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Acknowledgments -- 1. FOUNDATIONS OF PROBABILITY THEORY -- 1.1. Introductory notes -- 1.2. Some set theory and topology -- 1.2.1. Set theory useful in probability -- 1.2.2. Interesting topological spaces -- 1.3. Important family of sets in probability theory -- 1.4. Measurable spaces -- 1.5. Probability spaces -- 1.5.1. Infinite probability spaces -- 1.6. Filtration -- 1.7. Random variables -- 1.8. Integration with respect to a probability measure -- 1.9. Indicator functions |
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2.3.1. Invariant polynomials and elementary divisors -- 2.3.2. The Jordan canonical form -- 2.3.3. Remarks on the Jordan canonical form of a matrix -- 2.3.4. Construction of the transformation matrix of A to its Jordan form -- 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 |
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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 -- 3.3.1. A more advanced definition of a non-homogeneous Markov chain -- 3.4. The life and work of A.A. Markov -- 3.5. Probability distribution in the states of an NHMC -- 3.6. Examples -- 3.6.1. A more advanced result on the relation between a G-non-homogeneous Markov chain and martingales -- 3.7. Weak and strong ergodicity -- 3.8. Structures for coefficients of ergodicity |
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3.9. Conditions for weak ergodicity for general products -- 3.9.1. A synopsis of the life and mathematical legacy of Wolfgang Doeblin -- 3.9.2. General products of stochastic matrices -- 3.9.3. Consequences of the above general theorems to weak ergodicity of inhomogeneous Markov chains -- 3.9.4. An application of backward products in non-homogeneous Markov chains -- 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 |
| Notes |
Description based upon print version of record |
|
STRONG ERGODICITY |
| Form |
Electronic book
|
| ISBN |
9781351980708 |
|
135198070X |
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