Stochastic Processes I (8 ECTS)

Course Code: 
6126
Semester: 
3rd
Διδάσκων: 

CHARALAMBOS PAVLOPOULOS

Discrete probability spaces, probability generating functions, binomial models and Poisson limit theorems. Simple random walk, gambler’s ruin, game length, ballot theorems, arc-sine law. Markov chains, matrix of transition probabilities, classification of states. Asymptotic behavior, stationary distribution, stability equations. Time reversibility, Kolmogorov's criterion, random walks on graphs. Speed of convergence to stationary distribution, potential matrices. Perfect simulation and the Propp-Wilson algorithm. Branching processes and probability of extinction. Poisson process, Markov chains in continuous time, Kolomogorov’s differential equations, birth - death - migration process.

Recommended Reading

  • Χρυσαφίνου Ουρανία (2008) Εισαγωγή στις Στοχαστικές Ανελίξεις. Εκδόσεις Σοφία.
  • Cox, D.R. and Miller, H.D. (1965). Theory of Stochastic Process, Methuen, London.
  • Ross, S. M. (2002). Introduction to Probability Models, 8th edition, Academic Press.
  • 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.
  • Norris, J.R. (1998). Markov Chains, Cambridge University Press.

(old title: Stochastic Processes)

The course outline is here.