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Politecnico di Torino | |||||||||||||||||
Anno Accademico 2009/10 | |||||||||||||||||
01KRRHR, 01KRRBP, 01KRRCY, 01KRRGE, 01KRRHT, 01KRRKZ Stochastic processes |
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Corso di L. Specialistica in Ingegneria Telematica - Torino Corso di L. Specialistica in Ingegneria Delle Telecomunicazioni - Torino Corso di L. Specialistica in Ingegneria Informatica - Torino Espandi... |
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Esclusioni: 01GQS; 01JEV |
Obiettivi dell'insegnamento
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.
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Programma
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] |
Bibliografia
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 |
Verifica la disponibilita in biblioteca |
Controlli dell'apprendimento / Modalità d'esame
Written examination.
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Orario delle lezioni |
Statistiche superamento esami |
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