Area of Mathematics: Statistics-Probability-Operational Research (ESPOR)
Semester: 4ο
Course ID: 42301
Course Type: Elective
Teaching hours per week: Theory: 4 Practice: 0 Laboratory: 0
ECTS : 5
Eclass: For the course’s material, click here.
Instructors:
Description
- Basic notions from Probability Theory.
- About stochastic processes in general. Discrete-time Markov Chain. Transition probabilities matrix, Chapman-Kolmogorov equations. First passage (or return) probabilities and distribution of first passage (or return) time. State classification. Recurrent states, transient states, absorbing periodic states, aperiodic states. Classes of communicating states. Closed classes. The canonical form of the transition matrix. Limiting behavior of states, ergodic theorem, stationary distribution. Random walks. The Gambler’s Ruin.
- Continuous-time Markov Chains. Generator matrix, Kolmogorov equations, limiting behavior of states.
- Poisson process, birth-death process. Applications.
Bibliography
- Kulkarni V.G., Modeling and Analysis of Stochastic Systems. CRC Press, 2010
- Ross S.M., Introduction to Probability Models, Academic Press, 2009
- Lawer G.F., Introduction to Stochastic Processes, 2006
