Topicos Avanzados en Ing. Mat

Introduction to Stochastic Differential Equations

Announcements and other information about the class can be found here.

Instructor: Anastasios Matzavinos, amatzavinos@mat.uc.cl

Class meeting times: Mon & Wed 10:00 am - 11:20 am.

Instructor's office hours: Mon & Wed 2:00 pm - 3:00 pm or by appointment.

Course description: This semester, the focus of IMT 3800 will be on the theory and applications of stochastic differential equations. Topics covered will include Brownian motion and white noise, stochastic integration, the Itô calculus, existence and uniqueness of solutions to stochastic differential equations, and the Feynman-Kac formula. More advanced topics, such as Lévy processes, stochastic control theory, and inference for diffusion processes may be addressed depending on the interests of the class and time restrictions.

Learning outcomes: Stochastic differential equations have diverse applications in physics (Feynman-Kac formula), engineering (filtering and control theory), the financial markets (stock price modeling), and non-parametric statistics, among others. Upon successful completion of this course, students will be able to demonstrate the following competencies: (i) a working understanding of stochastic differential equations and the theory of Itô calculus, and (ii) the ability to further develop current applications of stochastic differential equations in engineering and mathematics.

Course textbook: We will mainly use the following reference.

• An Introduction to Stochastic Differential Equations by Lawrence C. Evans. American Mathematical Society, 2013.

Grading policy: The final grade will be based on homework assignments and a final take-home exam.

Homework assignments: Homework problems will be handed out on a regular basis. Discussion of homework assignments with other students is encouraged, but what is handed in should be your own work.