Stochastic Modeling 1st Edition by Nicolas Lanchier ISBN 3319500376 9783319500379

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ISBN 10:  3319500376
ISBN 13: 978-3319500379
Author:   Nicolas Lanchier 

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 gambler’s ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright –Fisher model, Kingman’s coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and Matlab™.

Stochastic Modeling 1st  Table of contents:

1. Basics of measure and probability theory
2. Distribution and conditional expectation
3. Limit theorems
4. Front Matter
5. Stochastic processes: general definition
   
6. Martingales
   
7. Branching processes
   
8. Discrete-time Markov chains
   
9. Symmetric simple random walks
   
10. Poisson point and Poisson processes
    
11. Continuous-time Markov chains
    
12. Front Matter
    
13. Logistic growth process
    
14. Wright–Fisher and Moran models
    
15. Percolation models
    
16. Interacting particle systems
    
17. The contact process
    
18. The voter model
    
19. Numerical simulations in C and Matlab
    
20. Back Matter

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