Overall objectives:

1 - To know the standard concepts and methods in the modeling using stochastic processes.
2 - To be able to prove and to use the most important results of the theory of stochastic processes.
3 - To be able to identify the models of stochastic processes most suitable for a particular problem in order to apply the theory of stochastic processes for modeling physical, biological, economic and social phenomena, among others.

Syllabus:

1 - Introduction
2 - Markov chains: Introduction
3 - The long term behaviour of Markov chains
4 - Poisson Processes
5 - Continous time Markov chains
6 - Queueing processes
7 - The Brownian motion and other related processes

Literature/Sources:

R. Durrett , 1999 , Essentials of Stochastic Processes , Springer
G. Grimmett, D. Stirzaker , 2001 , Probability and Random Processes , Oxford University Press
H. Taylor, S. Karlin , 1998 , An Introduction to Stochastic Modeling , Academic Press
S. Karlin, H. M. Taylor , 1975 , A first course in stochastic processes , Academic Press
S. Karlin, H. M. Taylor , 1981 , A second course in stochastic processes , Academic Press

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Lectures with the possibility of student participation. Theoretical-practical classes where students solve and discuss exercises and problems related to the contents of the course, with the guidance of the teacher, whenever necessary. The assessment includes two written tests, each worthing 40% of the final grade, and a report with oral presentation and discussion, worthing 20% of the final grade. The two tests aim to assess the theoretical and theoretical-practical knowledge acquired by the students. The report is carried out in groups of two students. It allows the student to develop skills in writing, presentation of results, oral communication and teamwork.