Description :

This is an introductory graduate sequence in stochastic processes. The course sequence is intended as an introduction to stochastic analysis for students of Mathematics, but also to students in Engineering, Economics or Finance that wish to sudy stochastic processes and their applications.
In Mathematics 271A the course sequence starts with basic notions of stochastic processes and an introduction to Brownian motion. Then we discuss important tools of modern stochastic calculus.
In mathematics 271B we study stochastic differential equations and diffusions in more detail. We discuss martingales and martingale problems.
Modeling in terms of a random environment is important in many contexts. In Mathematics 271c we discuss asymptotic analysis of stochastic ordinary differential equations and how this relates to analysis of various systems. In particular we discuss application to mathematical finance.

Math 271A

• Professor: Knut Solna; ksolna@math.uci.edu
• Office Hour: MWF after class
• Office: Rowland Hall 540G

Homework:

Approximately 5 homeworks will be assigned and collected in class.  No late homework will be accepted. Each homework assignment will have the same weight in the final grade.

Grading:

Overall course letter grades will be based on exam and homework according to the following weights:
Homework: 60%     Final: 40%

Prerequisites:

basic probability, multi-variate calculus, and differential equations.

Special Note:

The structure of the course is subject to change and will be adapted to the interest of the students; any changes will be announced in class.

Reference Books:

Karatzas and Shreve, Brownian Motion and Stochastic Calculus, Springer. Oksendal, Sochastic Differential equations, Springer.

Various:

You are responsible for the content of all course emails sent to your UCI account. These course emails could contain urgent information regarding new facts for a lecture or change of dates in the schedule. Once sent these become part of our contract of expectations. All students are required to activate their UCI netIDs. You can go to this website to activate your netID: https://ucinetid2.nacs.uci.edu/activate/menu.html.

I strongly adhere to the University's Academic Honesty policy, and cheating will NOT be tolerated. A student caught cheating may receive an F for the course and/or suffer other serious disciplinary action. Information for students regarding the UCI Academic Honesty policy can be found at: http://www.editor.uci.edu/catalogue/appx/appx.2.htm#gen0.

Tentative Syllabus 271A.

Homework # 1.

Homework # 2.

Homework # 3.

Homework # 4.

Homework # 5.