Stochastic processes PhD course

Weeks 6, 11 Linköping University Sweden

Exact dates still need to be set.

Page will be updated as more information becomes available

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.

Examination:

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

Past editions:

  1. spring 2024, Linköping University, Linköping, Sweden