Advanced Stochastic Processes II
STAT4404 Semester 1, 2013
Teaching Staff: Patricia Menendez (coordinator), Yoni Nazarathy
This course is designed to introduce diffusion processes as limits of stochastic processes arising in applied probability and statistics.
The course will start with a short introductory unit, motivating the analysis of stochastic processes of queues and illustrating how their limiting processes are diffusive. Followed by this, the course will cover martingales, Brownian motion and related diffusion processes. In addition, there will be computer simulations to illustrate examples of such processes. At this point (about half way in the course), the students will learn the functional central limit theorem for random walks and then move on to a variety of applications of stochastic process limits in queues and related processes. The stochastic process limits are mostly based on the continuous mapping theorem. Some contemporary research papers are introduced. During the final week of there course, there will be additional applications of stochastic processes limits arising in statistics.
The recommended pre-requisite for the course is STAT3004 or an equivalent course (i.e. a course in introductory random processes) as well as a course in mathematical analysis (e.g. MATH2400). In-depth knowledge of measure theoretic probability and functional analysis is not assumed. Needed concepts will be introduced as the material progresses.