Fall 2009: Theory of Probability I (M385C/CAM384K)

• First-day handout / course description
• Lecture notes: (files may change/be updated from time to time. Make sure to check the time-stamp in the footer. Beware of typos and more serious errors - these are still very much under construction. In fact, if you spot any mistakes of any kind, I would be very grateful if you sent me an e-mail. )
  • Measurable Spaces [09/20] (slides [08/27])
  • Measures [09/12] (slides [09/02])
  • Lebesgue integration [09/17] (slides [09/16])
  • Lebesgue spaces and inequalities [09/23] (slides [09/23])
  • Theorems of Fubini-Tonelli and Radon-Nikodym [09/28] (slides [09/28])
  • Basic Notions of Probability [10/11] (slides [10/12])
  • Weak Convergence of Probability Measures [10/22] (slides [10/19])
  • Characteristic functions [10/25] (slides [10/25])
  • WLLN and CLT [10/31] (slides [10/31])
  • Conditional Expectation [11/06] (slides [11/06])
  • Discrete Martingales [11/20] (slides [11/16])
  • Uniform Integrability and Martingales [11/17] (slides [11/18])
  The date in brackets is the last time a file has been updated. I try to keep up with typos I/you find in the lectures. Not so much for the slides.
• Homework assignments:
  • hw1 (with solutions)
  • hw2 (with solutions)
  • hw3 (with solutions)
  • hw4 (with solutions)
  • hw5 (with solutions)
  • hw6 (with solutions)
  • hw7 (with solutions)
  • hw8 (with solutions)
  • hw9 (with solutions)
  • hw10 (with solutions)
  • hw11 due on Fri, Dec 4, 2009
• Exams and Solutions:
  • Midterm: problems and solutions, statistics.

Spring 2009: Theory of Probability II (M385D/CAM384L)

• First-day handout / course description

Fall 2008: Introduction to Stochastic Processes (M362M)

• First-day handout

Spring 2008: Introduction to Stochastic Processes (M362M)

Fall 2007: Theory of Probability I (M385C/CAM384K)

• Course description
• First-day handout

Spring 2007: Topics in Stochastic Analysis (M393C/CAM393C)

• Course description
• Lecture notes (on discrete equilibrium theory):
  • Lecture 1
  • Lecture 2
  • Lecture 3
  • Lecture 4
  • Lecture 5
  • Lecture 6

Fall 2006: Theory of Probability I (M385C/CAM384K)

Spring 2006: Topics in Stochastic Analysis (M393C/CAM393C)

• Course description
• Lecture notes (very much under construction):
  • Introduction
  • Chapter 1 (Semimartingales)
  • Chapter 1 (problems)
  • Chapter 2 (Lévy processes)
  • Chapter 2 (problems)
  • Chapter 3 (financial markets)
  • Chapter 3 (problems)
  • Appendix A (a few facts from measure theory)
  • Appendix B (two theorems about martingales)
  • Bibliography (annotated)

Fall 2005: Matrices and Matrix Computations (M340L)

Spring 2005: Continuous-time Finance (at Carnegie Mellon University)

• A set of lecture notes (one large file)