Stochastic Processes ΙΙ (8 ECTS)

Markovian processes in continuous time and discrete state space. Generators, forward and backward Kolmogorov functions. Calculating transition probabilities. Birth – death processes and applications. Markjovian processes in discrete time with continuous state spaces.

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. Simulating stochastic processes. Applications in economics, finance, environment and contemporary technologies.

Recommended Reading

• Κουμουλλής Γ. Χ., Νεγρεπόντης Σ.,  Θεωρία Μέτρου, Εκδόσεις Συμμετρία, 2005.

• 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 συνεχούς 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.

The courses outline can be found here.