Stochastic processes PhD course

Weeks 6, 11 Linköping University Sweden

Venue:

Campus Valla, Building B, John von Neumann

Credits: 7.5hp

Registration:

Please contact me by email. If you are a PhD student of the Department of Computer and Information Science, Linköping University then please register through the PhD student's portal.

Content:

  1. Revision of selected parts of probability theory, in particular the moment generating function.
  2. Stochastic processes - definition and examples.
  3. Finite dimensional distributions of a stochastic process.
  4. Homogeneous and non-homogeneou Poisson processes.
  5. Markov chains, random walks, stochastic matrices.
  6. Branching processes.
  7. Martingales.
  8. Doob Theorem.
  9. Gaussian processes, Brownian motion.
  10. Kolmogorov Theorem.

Literature:

  1. G. Grimmett, D., Stirzaker, Probability and Random Processes, Oxford University Press, 2020.
  2. S. Ross, Stochastic Processes, John Wiley and Sons, 1996.
  3. (if you read Polish) J. Jakubowski, R. Sztencel, Wstęp do do teorii prawdopodobieństwa, SCRIPT, 2010.

Examination:

Will consist of solving exercises during the sessions and a take-home assignemnt at the end of the course.

Programme:

NB: Apart from the 9:15 start time, the times are approximate and may be dynamically adjusted!
NB: The long slots below will of course have breaks, which will be mutually decided on.
Block 1: February 2, Monday
TimeClassTopic
09:15-12:00Lecture 0Introduction to course and stochastic processes
12:00-13:15 Lunch break
13:15-15:00Lecture 1Probability recap (with breaks)
Block 1: February 3, Tuesday
09:15-12:00Lecture 2Examples of stochastic processes
12:00-13:15 Lunch break
13:15-15:00ExercisesSheet 1
Block 1: February 4, Wedensday
09:15-12:00Lecture 3Markov Chains
12:00-13:15 Lunch break
13:15-15:00ExercisesSheet 2
Block 1: February 5, Thursday
09:15-12:00Lecture 4Branching processes (part I)
12:00-13:15 Lunch break
13:15-15:00Reserve slot
Block 2: March 9, Monday
TimeClassTopic
09:15-12:00Lecture 4Branching processes (part II)
12:00-13:15 Lunch break
13:15-15:00Lecture 4Branching processes (part II, continued)
Block 2: March 10, Tuesday
09:15-12:00Lecture 5Martingales
12:00-13:15 Lunch break
13:15-15:00Lecture 5Martingales (continued)
Block 2: March 11, Wedensday
09:15-12:00Lecture 6Continuous time, continuous state stochastic processes
12:00-13:15 Lunch break
13:15-15:00ExercisesSheets 3,4
Block 2: March 12, Thursday
09:15-12:00Reserve slot
12:00-13:15 Lunch break
13:15-15:00Reserve slot

Past editions:

  1. spring 2024, Linköping University, Linköping, Sweden