Dettagli sull'Insegnamento per l'A.A. 2015/2016
Nome:
Stochastic Processes / Stochastic Processes
Informazioni
Crediti:
: Master Degree in Mathematical Engineering 6 CFU (b)
Erogazione:
Master Degree in Mathematical Engineering 1st anno curriculum Comune Elective
Lingua:
Inglese
![[info]](img/info16.png)
Prerequisiti
Probability theory (probability spaces, conditional probability, independence, product spaces, random variables and their distributions, expectation, convergence, limit theorems for sequences of random variables), real analysis, basics on measure theory and Lebesgue integral, basics on discrete times markov chains
Obiettivi
The course aims to give an introduction to the theory of stochastic processes with special emphasis on applications and examples. On successful completion of this module the students should become familiar with some of the most known classes of stochastic processes (such as martingales, markov processes, diffusion processes) and to acquire both the mathematical tools and intuition for being able to describe systems with randomness evolving in time in terms of a probability model and to analyze it charcterizing some of its properties
Sillabo
- Stochastic Processes: definition, finite dimensional distributions, stationarity, sample path spaces, construction, examples
- Filtrations, stopping times, conditional expectation.
- Markov processes: definition, main properties and examples. Birth and death processes.
- Poisson process with applications on queueing models.
- Martingales: definition, main properties and examples. Branching processes
- Brownian motion: definition, construction and main properties.
- Brownian Bridge, Geometric Brownian Motion, Ornstein-Uhlenbeck process.
- Ito integral and stochastic differential equations. Applications and examples
Descrittori di Dublino
Alla fine del corso, lo studente dovrebbe
- have knowledge of language, basic concepts and techniques of the Theory of stochastic processes, have knowledge and understanding of some relevant classes of processes (Markov processes, Martingales, Diffusions) and their properties, have knowledge and understanding of tha main mathematical tools and results on Stochastic calculus and be aware of its potential applications
- be able to identify, analyse and prove relevant properties of models based on stochastic processes, be able to solve problems related to such models
- evaluate the possible approaches to modeling a system with randomness using a stochastic process, be able to select the most appropriate one, to discuss its fundamental futures and to compare it with other models
- demonstrate ability to describe complex systems and problems in a probabilistic way, explain them in terms of stochastic dynamics, to illustrate and give rigorous proofs of their main features
- demonstrate capacity for reading and understanding texts and research papers on related topics
Testi di riferimento
- P. Billingsley, Probability and measure , John Wiley and Sons. Additional text
- G. Grimmett, D. Stirzaker, Probability and random Processes , Oxford University Press.
- B. Oksendal, Stochastic Differential Equations , Springer-Verlag .
Modalità d'esame
Written and oral exam.
Note
- Si veda anche la pagina sul vecchio sito di ingegneria: http://www.ing.univaq.it/cdl/scheda_corso.php?codice=I2W040
Aggiornamenti alla pagina del corso
Le informazioni sulle editioni passate di questo corso sono disponibili per i seguenti anni accademici:
Per leggere le informazioni correnti sul corso, se ancora erogato, consulta il catalogo corsi di ateneo.
Ultimo aggiornamento delle informazioni sul corso: 10 maggio 2016, 15:56
English version
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