Probability Theory II (Spring 2026)

Lectures: TuTh 11:00-12:15 WWH 517
Office hours: Fr 3:00-4:00 WWH 1013

Course on stochastic process for PhD students.

Schedule

Notes (updated after class)

  1. Stochastic processes in continuous time.
  2. Functions of bounded variation.
  3. Martingales in continuous time.
  4. Semimartingales.
  5. Kolmogorov's continuity theorem
  6. Definition of Brownian motion
  7. Heat equation and Feynman-Kac formula
  8. Strong Markov property and reflection principle

    9. Problem sets

    Grading

    Problem sets: 50%
    Final exam: 50%

    References

    • Varadhan, Stochastic Processes.