Stochastic Modeling. 1st ed. 2017

種類:

電子ブック

責任表示:

by Nicolas Lanchier

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Lanchier, Nicolas.
• SpringerLink (Online service)

シリーズ名:

Universitext ;

ISBN:

9783319500386 [3319500384]    

注記:

1. Basics of Measure and Probability Theory -- 2. Distribution and Conditional Expectation -- 3. Limit Theorems -- 4. Stochastic Processes: General Definition -- 5. Martingales -- 6. Branching Processes -- 7. Discrete-time Markov Chains -- 8. Symmetric Simple Random Walks -- 9. Poisson Point and Poisson Processes -- 10. Continuous-time Markov Chains -- 11. Logistic Growth Process -- 12. Wright-Fisher and Moran Models -- 13. Percolation Models -- 14. Interacting Particle Systems -- 15. The Contact Process -- 16. The Voter Model -- 17. Numerical Simulations in C and Matlab.
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the

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