Scheda programma d'esame
PROBABILITÀ
FRANCO FLANDOLI
Anno accademico2016/17
CdSMATEMATICA
Codice070AA
CFU6
PeriodoPrimo semestre
LinguaItaliano

ModuliSettoreTipoOreDocente/i
PROBABILITÀMAT/06LEZIONI60
FRANCO FLANDOLI unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge
Students will acquire a fair knowledge on the main ideas of probability: measure theory foundations, limit theorems, basic stochastic processes. Students will be able to analyse non--trivial problems involving probabilistic models.
Assessment criteria of knowledge
During the oral exam the student must be able to demonstrate his/her knowledge of the course material, to explain correctly the topics presented during the course and to discuss thoughtfully the main ideas.

Methods:

  • Final oral exam

Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures
  • individual study

Attendance: Advised

Teaching methods:

  • Lectures

Syllabus
Measure theory, integration, random variables, expected value, independence, 0-1 laws, Borel-Cantelli arguments. Laws, characteristic functions, convergence of random variables, tightness, Gaussian laws. Weak law of large numbers, strong law of large numebrs, central limit theorem, law of rare events. Conditional expectation, stochastic processes, Brownian motion
Bibliography
The course lectures cover all of the material and are taken from the following works that are also recmmended readings: * Pratelli, Un corso di calcolo delle probabilità. * Durrett, Probability theory and examples, 1991 * Karatzas, Shreve, Brownian motion and stochastic calculus, 1991. * Moerters, Peres, Brownian motion, 2010.
Work placement
Yes
Ultimo aggiornamento 14/11/2016 17:27