MAT 236A (Stochastic Dynamics) Fall 2012

MAT 236A (Stochastic Dynamics) Fall 2012 (CRN 43633)
MWF 11-11:50AM, 1128 Bainer

http://www.math.ucdavis.edu/~gravner/MAT236/

Course Materials, including Homework Assignments.

INSTRUCTOR:

Janko Gravner

Note: Please only use email in an emergency, e.g., if you are sick and you cannot reach me by phone. I will not reply to emails with questions about the class material, etc.

Off. Hrs: Mon. 12-1pm, Tue. 1-2pm, Wed. 12-1pm, or by appointment, at my office.

MSB (also known as Math) is the Mathematical Sciences Bulding.

PREREQUISITES:

A working knowledge of abstract analysis, such as abstract measures, Lebesgue measures, integrals, monotone and dominant convergence theorems, Fubini's theorem, and basics of differential equations.

Some knowledge of probability, such as: measurable spaces, σ-algebras, independence and conditional expectation, convergence of random variables and probability measures, normal distributions, strong law of large numbers and the central limit theorem.

Basic facts about stochastic processes in discrete time: martingales and Markov chains.

Much of the material above will be briefly reviewed when needed; be prepared to do some additional reading if you have not seen some of the above topics. No economics background is necessary.

TEXTBOOK: Stochastic Calculus and Financial Applications, by J. Michael Steele (Springer, 2010).

GRADE: Course grade will be based on homework, which will be assigned about once a week and will be due in 7 days. No late homework will be accepted. You may discuss homework problems with me and other students from the class, but everything you turn in should be your work.

I do not give the grade I (Incomplete) under any circumstances; also, the grade NS (Enrolled No Work Submitted) no longer exists.

ADDITIONAL MATERIAL:

There are a great many free resources available on the web:

Myron Hlinka at University of Winsdor has an excellent aggregator site. Among the links are lecture notes by Lawrence Evans from Berkeley.

Two good survey papers on numerical solutions of stochastic differential equations are Desmond Higham and by Tim Sauer.

Other recommended books:

Probability with Martingales, by David Williams (Cambridge, 1991), is a good book to brush on probability background.
Brownian Motion and Stochastic Calculus, by I. Karatzas and S. E. Shreve (Springer, 1991), contains full mathematical details on topics related to this course.
Numerical Solution of Stochastic Differential Equations, by P. E. Kloeden and E. Platen (Springer 2010, first published in 1991), is a classic on its topic.
Stochastic Differential Equations: An Introduction with Applications, by B. Oksendal (Springer, 2010), is often used as textbook for this course.
Arbitrage Theory in Continuous Time, by Tomas Bjork (Oxford, 2009), is oriented towards financial applications.

If you want a math department computer account, please visit the class accounts page. You will have access to MATLAB, which is used for almost all computations I do for this class.

MAT 236A (Stochastic Dynamics) Fall 2012 (CRN 43633) MWF 11-11:50AM, 1128 Bainer

MAT 236A (Stochastic Dynamics) Fall 2012 (CRN 43633)
MWF 11-11:50AM, 1128 Bainer