Course Information:

Instructor: William L. Kath, Tech M460, x1-8784,

Class hours: MWF 10-11 in M416

Office hours: M 11-12, T 4-5, Th 10-11 or by appointment

There is no required textbook. Course notes will be available for the majority of the material.

The following references are available online and may be useful. The book by Kay is primarily on probability for those who would like more information than the review given at the beginning of the course. It has the advantage of of using Matlab throughout. The book by Asmussen and Glynn is a good general reference for many of the topics covered in the course. The book by Kloeden et al. is focused on numerical solution of stochastic differential equations and the book by Schuss goes into more depth on the theory of such equations.

1. Steven M. Kay, Intuitive Probability and Random Processes Using MATLAB
   
   https://search.library.northwestern.edu/permalink/01NWU_INST/h04e76/alma9980931120302441
2. Søren Asmussen and Peter W. Glynn, Stochastic simulation: algorithms and analysis
   https://search.library.northwestern.edu/permalink/01NWU_INST/h04e76/alma9980929219602441
3. Peter E. Kloeden, Eckhard Platen and Henri Schurz, Numerical Solution of SDE Through Computer Experiments
   https://link.springer.com/book/10.1007/978-3-642-57913-4 (you will need to be on NU's network for this link to work)
4. Zeev Schuss, Theory and applications of stochastic processes: An analytical approach
   https://search.library.northwestern.edu/permalink/01NWU_INST/h04e76/alma9980927091902441
   

Grading: There will be a number of Matlab-based computer projects throughout the course (with maybe a few analytical problems added).

Course Topics:

Analysis and implementation of numerical methods for random processes: random number generators, Monte Carlo methods, Markov chains, stochastic differential equations, and applications. Topics include:

1. Review of probability; random variables
2. Random number generators
   
3. Metropolis algorithm
4. Monte-Carlo integration
   
5. Importance sampling
   
6. Ising model
7. Markov processes
8. Birth and death processes
9. Random walks
10. Gillespie algorithm and approximations
11. Introduction to stochastic differential equations
12. Diffusion approximation and Fokker-Planck equations
13. Ito and Stratonovich calculus
14. Langevin equations
15. Numerical methods for stochastic ordinary differential equations
    
16. Large deviation theory
17. Numerical methods for stochastic partial differential equations (if time permits)