All readings will be listed here, organized by topic. Dates indicate
the class by which you should have read the indicated material.
Some readings may be announced here before they are announced in class,
in case you want to read ahead. Sometimes, particularly if
I am traveling, you may find some references posted at the library class
reserves before they are linked here.
If a reading does not have a date, you don't have to worry about it
yet.
Assigned Readings
Assigned Readings
Lawler, Intoduction to Stochastic Processes, Ch. 1 (PDF) (03/08/04) Optional Readings
- Resnick, Adventures in Stochastic Processes, Secs. 2.12-2.15 (PDF)
- Complete proof of existence and uniqueness of stationary distribution, and law of large numbers for Markov chains. Also some further discussion of recurrence/transience classification techniques and computational techniques for stationary distribution.
- Karlin & Taylor, A First Course in Stochastic Processes, App. 2 (PDF)
- Perron-Frobenius theory for positive matrices
- Haken, Synergetics, Secs. 4.6-4.8 (PDF)
- Stationary distributions: Detailed balance, microreversibility, and Kirchoff's method of solution
- Guttorp, Stochastic Modeling of Scientific Data, Sec. 2.1 (PDF)
- Maximum likelihood method for choosing parameters in Markov chain
- Bhat & Miller, Elements of Applied Stochastic Processes, Sec. 2.1 & 2.6 (PDF)
- Method for calculating variance of first hitting times, and application to delinquent credit management
- Resnick, Adventures in Stochastic Processes, Secs. 2.5-2.6 (PDF)
- Dissection principle for Markov chains and some theory on recurrence and transience when the n-step probability transition densities can be computed explicitly.
Assigned Readings
Lawler, Intoduction to Stochastic Processes, Ch. 2 (PDF) (03/25/04) Karlin & Taylor, A First Course in Stochastic Processes, Ch. 2 and 3 (PDF) (03/22/04)
Assigned Readings
Lawler, Intoduction to Stochastic Processes, Ch. 3 (PDF) (04/01/04) Andersson and Britton, Stochastic Epidemic Models and Their Statistical Analysis, Ch. 2 (PDF) (04/12/04) Optional Readings
- Reichl, A Modern Course in Statistical Physics, Ch. 5 (PDF) (PDF file may still be corrupted)
- A concise discussion of Markov chains and stochastic differential equations from a physicist's perspective. A nice collection of concepts, but there are some misleading statements!
Assigned Readings
Karlin & Taylor, A First Course in Stochastic Processes, Sec. 6.1-6.4 (PDF) (04/12/04)
Assigned Readings
Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Sec. 1.7,1.8 (PDF) (04/19/04) Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Sec. 2.3,2.4 (PDF) (04/22/04) Optional Readings
Friedman, Stochastic Differential Equations and Applications, Ch. 2
Assigned Readings
Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Ch. 3 (PDF) (04/30/04)
Optional Readings
Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Ch. 4.1, 4.5, 4.6, 4.8, 4.9 (PDF) Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Ch. 6.1, 6.3 (PDF)
Assigned Readings
Higham, "An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations," SIAM Review 43 (3), 525-546 (2001)
Optional ReadingsAlmgren, "Financial Derivatives and Partial Differential Equations," American Mathematical Monthly 109 (1), 1-12 (2002)