Stochastic Processes I (8 ECTS)

Course Code: 

Probabilities in discrete spaces, probability generating functions, binomial standards and Poisson limit theorems. The random walk, gamblers ruin, game length, poll theorems, arcsine law. Markov chains, probability table, transition, situation ranking. Asymptotic behavior, stationary distribution, balance functions. Kolmogorov's criterion, random walks in graphs. Convergence rate in a stationary distribution, πίνακες δυναμικού, perfect simulation and the Propp-Wilson algorithm. Branching processes and extinction probability. The Poisson process. Continuous Markov chains, differential Kolomogorov functions, 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)