MATH 303

Syllabus: pdf

Outline:

  • January 6: Motivation (slides)/ Discrete Time Markov chains (Markov property, transition matrix, notes)
  • January 8: Stationary distribution, transition diagram, Chapman-Kolmogorov equations (notes)
  • January 10: Classification of states: accessibility, communicating classes, period (notes)
  • January 13: Transient and recurrent states (notes)
  • January 17: Transient and recurrent states, Gambler’s ruin problem (notes)
  • January 20: Gambler’s ruin problem, Recurrence of random walk on Z (notes)
    – Some references on difference equations:  for the method with order 2, you can follow this link; to go deeper: classical reference (book), or this link, which makes the connection with linear algebra.
    – On the Stirling formula: see this link for a derivation, or for more complete expansion, here
  • January 22: Recurrence of random walk on Z^d (notes)
  • January 24: Recurrence of random walk on Z^d (notes)
  • January 27: Limiting Probabilities (notes)

Homework: