Course Details for A.Y. 2017/2018

The information on this page refer to the academic year 2017/2018. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2017/2018

Name:

Probabilità e Processi Stocastici 1 / Probability e Stochastic Processes 1

Type:

Module

Main course:

Probabilità e Processi Stocastici / Probability and Stochastic Processes

Basic information

Code:

DT0128

Sector:

Credits:

: Master Degree in Mathematics 6 CFU (b)

Term:

1^st semester

Degree(s):

Master Degree in Mathematics 1^st anno curriculum Generale Compulsory

Language:

English

Teacher(s):

Davide Gabrielli

Propaedeutics:

Probability

Course Objectives

To learn the fundamentals results concerning convergence of random variables, discrete time martingales and Poisson porcess

Course Content

Convergences of random variables and their implications. Borel Cantelli Lemmas. Uniform integrability
Conditional expected values, discrete time martingales. Hoeffdinf inequality, stopping times, martingale convergence Theorem, optional stopping Theorem,inequalities.
Poisson process and its properties. Construction using exponential random variables in the one dimensional case and with uniform and Poisson random variables in the general case. Applications

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

Acquiring knowledge and understanding of the basics tools of convergence of random variables, martingale theory and Poisson process
The student should be able to apply the theory studied in solving concrete problems
Making informed judgements and choices on the suitable models and approximations
The student should be able to comunicate and explain the topics included in the program of the course
The student should be able to read textbooks in probability and be able to increase its knowledge alone.

Prerequisites and Learning Activities

Basic notions of elementary probability theory

Assessment Methods and Criteria

Written and oral examination

Textbooks

G. R. Grimmett, D. Stirzaker, Probability and random processes, second edition , Oxford University Press. 1992.
G. R. Grimmett, D. Stirzaker, Probability and random processes. Problems and solutions , Oxford University Press. 1992.

Internet Resources

Homepage:

http://mat.univaq.it/~gabriell/didattica/2013-14/PPS1/PPcorso.html

Course page updates

This course page is available (with possible updates) also for the following academic years:

To read the current information on this course, if it is still available, go to the university course catalogue .

Course information last updated on: 24 ottobre 2017, 12:58