Course Material for Topics in Probability and Ergodic Theory

Lecture Notes

  1. Chapter 1, postscript file: Probability Spaces and Independence
  2. Chapter 1, PDF file
  3. Chapter 2, zipped postscript file: Random Variables
  4. Chapter 2, PDF file
  5. Chapter 3, zipped ps file Laws of Large Numbers. (Attention to the typos! A revision is in progress.)
  6. Chapter 3, pdf file
  7. Chapter 3, section F Stationary processes and the ergodic theorem (pdf)
  8. Chapter 4, zipped ps file Convergence in Distribution and the Central Limit Theorem.
  9. Chapter 5, Conditional expectation, ps file
  10. Chapter 5, pdf file
  11. Chapter 6, Martingales and Applications, pdf file
  12. Chapter 6, Martingales in Discrete Time, ps.gz file

Problem Sets.

  1. Problems 1-6 (corrected), postscript file.
  2. Comments on solutions to first problem set. (ps file)
  3. Problems 7-11, postscript file.
  4. Problems 12-17, postscript file.
  5. Problems on Chernoff/Hoeffding bounds, postscript file.
  6. Problems 18-24, postscript file.