AMCS 390G Special Topics in Advanced Probability

Lecture times: This course is held from January 2020-May 2020. Lecture times are at 1030-1200, Sunday and Wednesday. The notes are available on blackboard.

Office Hour: My office hour is at 1400 on Wednesday in my office 4112, building 1. I am not available at other times, unless there is a time-table clash, in which case, please contact me by email to arrange a meeting.

Assessed Coursework: During the course there will be two assignments which make up 40% of the final grade; you are given 2 weeks to complete each piece of work. The dates of when these assessments will be handed out will be provided at least 2 weeks beforehand.

Exam:. There is a closed book 2 hour final exam of four questions each of 20 marks. I do not give out formula sheets, but you are allowed one page of A4 cheat sheet. That is, a handwritten or typed sheet with any information you deem useful for the exam.

Problem Sheets: There are also 3 non-assessed problem sheets, to be handed out during the course. Once the classes are complete, typed solutions will be made available.

Course Details: These notes are not sufficient to replace lectures. In particular, many examples and clarifications are given during the class. The course is a first graduate course on measure theoretic probability, divided in the following chapters

  • Introduction to measure theoretic probability
  • Convergence theory
  • Martingales

Throughout the course, we will try to emphasize real applications, especially in the context of numerical methods that are found in applied mathematics and statistics. Mathematical formality is important, but, we will try to keep this to the minimum level required to understand the subject. It is expected that you will have a background in real analysis, calculus and linear algebra prior to the course and any undergraduate probability will be most useful. This course will be of use when studying stochastic processes, such as Markov chains. In the main, this course is relevant for discrete-time processes, although much of the theory lies at the roots of processes in continuous time or infinite dimension.

References: There is not a single recommended reference for this course, but the following texts will be very useful: [1, 2, 4, 5].