This course introduces the theory and applications of several important stochastic processes. The course mainly includes Markov chains, Poisson process and Brownian motion.

Course Materials

• Syllabus
• Slides:
  • 0: Introduction to R * 1: Poisson Process * 2: Markov Chain
• Notes: * 1: Poisson Process * 2: Markov Chain
• Assignments: * Assignment 1 * Solution, R file * Assignment 2 * Solution, R file

Course Outline

• Primer of statistics and probabilities
  • Introduction to probability theory
  • Random variables, expectations and conditioning
• Counting process
  • Poisson process
  • Renewal process
• Markov chains
  • Transition matrix
  • Classification of states

Grading

• Class participation: 10%
• Assignments: 20%
• Group project: 30%
• Thesis: 40%