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M850: Theory of Probability, Fall 2012

Instructor: Nayantara Bhatnagar
Class Times: MWF 14.30 - 15.20, Smith 201
Web page: https://sites.google.com/site/nayantarabhatnagar/home/m850f12

Final: TBA

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Office Hours: Fri 1-2 pm, 528 Ewing.

Prerequisites: M602 or M631. Permission is needed to attend otherwise.

References:  I will mostly follow lecture notes by Amir Dembo:
http://www-stat.stanford.edu/~adembo/stat-310c/lnotes.pdf

The main reference text will be R. Durrett, Probability : Theory and Examples, 4th ed.

Additional standard textbooks that can be useful as reference are:
P. Billingsley, Probability and Measure
D. Williams, Probability with Martingales

Topics: The course will cover the following topics, with the caveat that some changes are possible as needed.
  • A brief review of measure theory
  • Measure theoretic formulation of probability theory
  • Laws of large numbers
  • Notions of covergence
  • Central Limit Theorem
  • Conditional distributions, conditional expectation
  • Discrete time martingales
  • Introduction to Brownian motion and properties

   
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