GENERIC

This class is the continuation of Probability Theory I (STAT G6105) for Statistics PhD students.

Our main topic will be stochastic processes. Distributions of stochastic processes are essentially probability measures on infinite-dimensional spaces, and we will have to learn basic analysis and measure theory on such spaces as we go along. Other topics include condtioning and martingales.

Many of these concepts are also of great importance in statistics—infinite-dimensional spaces are the natural habitat of nonparametric models, conditioning is the principal tool of Bayesian statistics, and so forth—and I will try to highlight connections between probability and statistics wherever possible.

Final Exam

Monday, 11 May 2015, 9:00am,
in the class room (Math 407).
The exam will take ca two hours.

The exam is closed book. We will provide you with paper and a copy of the class notes.

Course Specs

Time: Mondays and Wednesdays, 10:10-11:25am.
Room: Mathematics 407.
Requirements: Probability Theory I.

Teaching Assistant

TA: Morgane Austern (ma3293).
Office hours: Tuesdays, 1:00-2:00pm, 10th floor SSW.

Class Notes

Homework

Tentative Syllabus

I may change the syllabus during the term; at present, it also still depends on how much material will be covered in Probability Theory I. Here is a (very) tentative list of topics:
  1. Conditional expectations and martingales
  2. Measures on metric spaces
  3. Conditioning and disintegration
  4. Weak convergence and spaces of probability measures
  5. Compactness and tightness
  6. Construction of stochastic processes
  7. Continuity of paths and Brownian motion
  8. Poisson processes, stationarity and Lévy processes
  9. The Itō integral
If time suffices, we may also be able to cover some of the following:
  • Markov processes and elementary ergodic theory
  • Banach spaces, Riesz representations, and $L_p$ spaces