2012S STA4247 Point Processes, Noise and Stochastic Analysis

From TorontoMathWiki

Course Information

Official description: Statistics 4247

Class schedule: Tuesday-Thursday 9:30-11 in Sidney Smith (SS) 2127. Starts Tuesday, January 10 2012.

Course Outline

Introduction to the theory of point processes – Poisson and compound processes, point provesses with repulsion and attraction. Brownian motion, white noise. Stochastic intergration and stochastic differential equtions.

Topics:

Determinantal and permanental processes
Random analytic functions and their zeros
Brownian motion, construction and path properties
White noise and other noises
Skorokhod's embedding
Blackwell's proof of the CLT and Donsker's theorem
Kolmogorov-Chentsov theorem
Law of iterated logarithm
Levy's modulus of continuity
Stochastic integrals (first with no theory), Ito's formula, change of variables
L2 theory of stochastic integration
Cameron-Martin formula

Textbook

See the January 10 lecture notes for information regarding the recommended readings.

Assignments

There will be problem sets.

Evaluation

Take-home exam due April 25 11:59am

Lecture Notes

Lecture notes will be handled by Andrew Stewart. While typing up lecture notes is not mandatory for the course, it is encouraged. Ideally, LaTeXed notes should be better than notes taken in class -- someone who isn't taking the class should be able to understand them. They should also be submitted in a timely manner -- ideally within three or four days of the class.

Please use the template provided below for typing the course notes. There are some instructions inside, so please read and follow them. Email the .tex source file and the compiled pdf file (so it's proven that it compiles) to andrewg (dot) stewart at utoronto (dot) ca.

Here is the template. There are some instructions in the template. In particular, please use the macros specified in the preamble, and try to use the labels that are consistent with previous lectures.

Here are the lecture notes uploaded thus far. Feel free to email either the author or Andrew about errors or mistakes.

January 10 (Andrew)

January 12 (Ali) <-- not fully edited.

January 17 (Andrew) (some examples missing)

January 19 (Ben) (unedited)

January 24 (Jeremy) (unedited)

January 26 (No one)

January 31 (Mustazee) (unedited)

February 2 (Ali) (unedited)

February 7 (Andrew) (unedited)

February 9 (Danny)

February 14 (Andrew) (unedited)