Stochastic Procedures ΙΙ (8 ECTS)

Course Code: 
Elective Courses

Martingales in discrete time, stopping times, filtrations (intuitive). Optional Stopping Theorem. Stochastic procedures in continuous time.  Brownian motion and its properties. Geometric Brown motion and the Ornstein-Uhlenbeck process. Gaussian processes. Introduction to the stochastic integral.

       Recommended Reading

  • Karlin S., Taylor H. M. (1981). A second course in stochastic processes, Academic Press.
  • Rogers L. C., Williams D. (2000). Diffusions, Markov processes and Martingales:Volume I, Foundations. Cambridge University press.
  • Revuz D., Yor M. (2004). Στοιχηματικές στοχαστικές διαδικασίες συνεχους χρόνου και κίνηση Brown (ελληνική μετάφραση), Leaders Books.
  • Χρυσαφίνου Ουρανία (2008) Εισαγωγή στις Στοχαστικές Ανελίξεις. Εκδόσεις Σοφία.
  • Karlin S. and H. Taylor (1975). A First Course in Stochastic Processes, Academic Press.
  • Grimmett, G.R. and D.R. Stirzaker (2001). Probability and Random Processes. Oxford University Press.
  • Steele, M.J. (2001). Stochastic Calculus and Financial Applications. Springer.