Presentazione

Organizzazione della Didattica

DM270
SCIENZE STATISTICHE ORD. 2014


9

Corsi comuni

 

Frontali Esercizi Laboratorio Studio Individuale
ORE: 64 0 0 69

Periodo

AnnoPeriodo
I anno1 semestre

Frequenza

Facoltativa

Erogazione

Convenzionale

Lingua

Inglese

Calendario Attività Didattiche

InizioFine
01/10/201620/01/2017

Tipologia

TipologiaAmbitoSSDCFU
affine/integrativo Nessun ambitoMAT/066
affine/integrativo Nessun ambitoMAT/053


Responsabile Insegnamento

ResponsabileSSDStruttura
Prof.ssa GIUMMOL FEDERICASECS-S/01

Altri Docenti

DocenteCoperturaSSDStruttura
Dott.ssa CESARONI ANNALISAAffidamentoMAT/05Dipartimento di Scienze Statistiche

Attività di Supporto alla Didattica

Non previste.

Bollettino

Sequences of real numbers: limit of a sequence, Cauchy sequences, subsequences. Series of real numbers: convergence and convergence criteria. Differential and Integral Calculus in R and in R^n.



Functional Analysis (3CFU) - Convergence notions for sequences of functions. Functions series: power series, Taylor series, Fourier series. - Measure theory: Caratheodory construction of a measure. Examples: the Lebesgue measure, the Lebesgue-Stieltjes measure, robability measures in continuous and discrete spaces. The definition of integral in a measure space. In particular: the Lebesgue integral. - Functions spaces Ck, Lp,W 1,p: definitions and basic properties. Hilbert spaces: definitions and basic results. The space L2. Probability Theory (6CFU) - Probability Distributions - Conditioning - Characteristic and moment generating functions - Functions of random variables - Normal distribution theory - Convergence of Random Variables - Central Limit Theorem - Further topics - Discrete time Markov chains - Continuous time Markov chains - Poisson process and Brownian motion

Written exam.


CONTENUTO NON PRESENTE

For Functional Analysis - Fusco, Marcellini, Sbordone, Analisi Matematica 2, Liguori - Kreyszig, Introductory functional analysis with applications, Wiley - Friedman, Foundations of modern Analysis, - Dover Brezis, Analisi Funzionale, Liguori - Rudin, Real and complex analysis, Mc Graw-Hill - Rudin, Functional Analysis,Mc Graw-Hill For Probability Theory A. Gut, An intermediate course in probability, Springer Verlag, 1995. J.R. Norris, Markov chains, Cambridge University Press, 1997. T.A. Severini, Elements of distribution theory, Cambridge University Press, 2005. S.I. Resnick, Adventures in Stochastic Processes, Birkhauser, 1992.