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Markov Processes: Characterization and Convergence.

Andris Abakuks, S. N. Ethier, Thomas G. Kurtz

Open publisher page 4,506 citations

Abstract

Introduction. 1. Operator Semigroups. 2. Stochastic Processes and Martingales. 3. Convergence of Probability Measures. 4. Generators and Markov Processes. 5. Stochastic Integral Equations. 6. Random Time Changes. 7. Invariance Principles and Diffusion Approximations. 8. Examples of Generators. 9. Branching Processes. 10. Genetic Models. 11. Density Dependent Population Processes. 12. Random Evolutions. Appendixes. References. Index. Flowchart.

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What this paper is about

Introduction. 1. Operator Semigroups. 2. Stochastic Processes and Martingales. 3. Convergence of Probability Measures. 4. Generators and Markov Processes. 5. Stochastic Integral Equations. 6. Random Time Changes. 7. Invariance Principles and Diffusion Approximations. 8. Examples of Generators. 9. Branching Processes. 10. Genetic Models. 11. Density Dependent Population Processes. 12. Random Evolutions. Appendixes. References. Index. Flowchart.

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Available abstract

Introduction. 1. Operator Semigroups. 2. Stochastic Processes and Martingales. 3. Convergence of Probability Measures. 4. Generators and Markov Processes. 5. Stochastic Integral Equations. 6. Random Time Changes. 7. Invariance Principles and Diffusion Approximations. 8. Examples of Generators. 9. Branching Processes. 10. Genetic Models. 11. Density Dependent Population Processes. 12. Random Evolutions. Appendixes. References. Index. Flowchart.

Key concepts: Markov chain, Mathematics, Markov process, Applied mathematics, Convergence (economics), Stochastic process, Weak convergence, Characterization (materials science)

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