Course Details for A.Y. 2016/2017

The information on this page refer to the academic year 2016/2017. 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:

2016/2017

Name:

Stochastic Processes / Stochastic Processes

Type:

Course

Basic information

Code:

DT0052

Sector:

MAT/06

Credits:

: Master Degree in Mathematical Engineering 6 CFU (b)

Term:

2^nd semester

Degree(s):

Master Degree in Mathematical Engineering 1^st anno curriculum Comune Elective

Language:

English

Teacher(s):

Ida Germana Minelli

Course Objectives

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

Course Content

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

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

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

Prerequisites and Learning Activities

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

Assessment Methods and Criteria

Written and oral exam.

Textbooks

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 .

Notes

Si veda anche la pagina sul vecchio sito di ingegneria: http://www.ing.univaq.it/cdl/scheda_corso.php?codice=I2W040

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: 10 maggio 2016, 15:56