STAT 8540 - Topics in Advanced Stochastic Processes

Statistical Inference for Stochastic Differential Equations



Class notes
References
Computing


Class information
Location: Lecture: TR 9:35am – 10:55am, Scott Lab E241.
Office hours: CH223, W 12:30pm-2:30pm, and by appointment.

References:

  • Statistics of Stochastic Processes I and II by R.S. Lipster, A.N. Shiryaev and B. Aries, Springer, 2000;

  • Statistical Inference for Ergodic Diffusion Processes by Y. Kutoyants, Springer, 2010;

  • Brownian Motion and Stochastic Calculus by I. Karatzas and S. Shreve, Springer, 1991;

  • Probability and Measure, by Patrick Billingsley, Wiley,1995.

Course description and objectives
Stochastic differential equations (SDEs) model the stochastic evolution of a system as time evolves. These models have a variety of applications in many disciplines (economics, mathematical finance, biology, genetic analysis, oceanography, ecology, etc.) and emerge naturally in the study of many phenomena. This course will introduce the audience to the fundamental concepts used in SDEs, with emphasis on statistical estimation in the parametric and nonparametric setting. Structurally the course will be divided in three parts: 1) a primer on stochastic processes, stochastic calculus and stochastic differential equations; 2) estimation methods for SDEs accompanied by numerical simulations and 3) applications and case studies.

Prerequisites
Students are expected to have a minimal understanding of differential equations, sufficient background in advanced probability (STAT 7201 or equivalent), advanced inference and basic knowledge of a scientific programming language.

Evaluation
Evaluation will be based on in-class participation (30%) and two take-home assignments (70%).

Attendance policy
It is strictly required to attend all the classes. It is the student’s responsibility to make up for the material covered in class during any absence.

Special accommodations
If you need any accommodations based on the impact of a documented disability, contact the instructor privately to discuss specific needs, within a week. You should also contact the Office of Disability Services to coordinate special accomodations.

Academic misconduct
Academic misconduct will not be tolerated and will be dealt with procedurally in accordance with university policy.