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Politecnico di Torino
Academic Year 2007/08
01KRRHR, 01KRRBP, 01KRRCY, 01KRRHT, 01KRRKZ
Stochastic processes
Master of science-level of the Bologna process in Computer And Communication Networks Engineering - Torino
Master of science-level of the Bologna process in Telecommunication Engineering - Torino
Master of science-level of the Bologna process in Computer Engineering - Torino
Espandi...
Teacher Status SSD Les Ex Lab Tut Years teaching
Pistone Giovanni       3 2 0 0 4
SSD CFU Activities Area context
MAT/06 5 C - Affini o integrative Cultura scientifica, umanistica, giuridica, economica, socio-politica
Esclusioni:
01JEZ
Objectives of the course
This course is designed to review basic concepts in probability and to introduce to topics in stochastic processes which are expecially relevant for applications involving discrete quantities, eg counts.






Syllabus

1. Recap of basic probability. Probability space, random variables,
expectation, notable distributions, joint distribution,
conditioning (Ross ch. 1-3); Simulation: inverse method, rejection
method, variance reduction, point processes (Ross ch. 11). [15 h]

2. Markov chains, discrete time. transitions, classification of
states, stationarity and ergodicity, time reversibility,
Monte-Carlo-Markov-Chain methods. Examples. (Ross ch 4). [10 h]

3. Poisson process: equivalent definitions, generalizations
(non-homogeneous, compound, mixed). Examples. (Ross ch 5). [10 h]

4. Markov chains, continuous time. Transitions, birth and death
processes, reversibility. (Ross ch 6). [15 h]

5. Topics in renewal theory. (Ross ch 7-8). [10 h]

Bibliography

Sheldon N. Ross "Probability Models" 8th ed Academic Press

Other suggested readings:

Sheldon N. Ross "Stochastic processes" 2nd ed John Wiley

Pierre Bre'maud "Markov Chains, Gibbs Fields, Monte Carlo
Simulation and Queues" Springer 1999
Revisions / Exam
Written examination.

Programma definitivo per l'A.A.2009/10
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