Advanced Topics in Stochastic Processes
Sustainable Development Goals
Learning Goals
The main objective is to provide fundamental theoretical concepts to the modeling of stochastic systems and develop in students the ability to use the most common types of stochastic processes. It is intended that the students acquire the fundamental theoretical concepts of stochastic processes and their importance in the analysis of stochastic phenomena.
Contents
1. Poisson processes and its variants.
2. Renewal processes and its variants..
3. Networks of queues and applications to the modeling of telecommunications systems.
4. Diffusion process and Wiener process, Brownian motion.
5. Ito and Stratonovich stochastic integrals, Ito's formula.
6. Stochastic differential equations and its application to modeling animal population growth and financial data.
Teaching Methods
Tutorial sessions of theory and exercises
Introduction to theoretical concepts and practical exercises using examples in several areas, thus seeking to sensitize students to the importance of the exposed topics.
In the e-leaarning version, in case there are students registered for the e-learning regimen, use of a Moodle platform and synchronous and asynchronous contacts.
Assessment
1. Priviledge a continuous evaluation system through two individual assignements (typically the resolution of exercises and problems), a final test (with the requirement of a minimum grade of 7 "valores" out of 20) and an individual project. The grade will be the weighted average of these 4 items, the 2 assigments having together a weight of 1/3 (each having a weight of 1/6), the project having the weight 1/3 and the test having also the weight 1/3.
In case of no approval under this continuous evaluation system, the student should do an exam, but the project is still mandatory.
For students registered in the e-earning regimen, the evaluation follows a specific format to be indicated in the Moodle platform if there are students under that regimen.
The project should be delivered in the Moodle platform of the curricular unit up to the date indicated below. It can consist on the application of models using real-life data or simulation studies on the analysis and criticism of a relevant paper published in a scientific journal (topics/paper to be selected in agreement with the teacher and proposed before December 6, 2016). The project should preferably be delivered in pdf format and, in case it has supporting extensive numerical computations or simulations, these should be delivered as well through their corresponding computing files (either a spreadsheet, the program and output in R language or some other format agreed with the teacher).
2. The students can choose a Non-continuous Evaluation system, having available an exam and a make-up exam. The student that falis some requirement for the continuous evaluation system, can use the non-continuous evaluation system. The delivery of the individual project is mandatory even with the non-continuous evaluation system, and it weights 1/3 of the the final classification, the exam having the other 2/3 of the weight.
Evaluation Schedule:
Deadline to agree with the teacher on the topic/paper of the individual project: December 6, 2016
Deadline for delivery of the individual project through the Moodle platform of the curricular unit: January 9, 2017
Test: January 7, 2017, 10h-13h. Location: sala 125 CLAV
Exam - normal epoch: January 17, 2017, 10h-13h. Location: sala 066 CLAV
Exam - make-up epoch: January 25, 2017, 10h-13h. Location: sala 126 CLAV
Exam- special epoch: July 6, 2017, 10h-13h
Exam - extraordnary epoch: July 14, 2017, 10h-13h
NOTE: In the test and in the exams, students can consult their notes.
Recommended Reading
Mais utilizada:
Arnold, L. (1974). Stochastic Differential Equations: Theory and Applications. Wiley, N.Y.
*Braumann, C.A. (2005). Introdução às Equações Diferenciais Estocásticas, Edições SPE, Lisboa
Øksendal, B. (2003). Stochastic Differential Equations. An Introduction with Applications (6th edition). Springer-Verlag, Berlin
Feller, W. A. (1968). An Introduction to Probability Theory and its Applications, Vol. I (3rd ed.) e Vol. II (2nd ed.). New York.
*Karlin, S. and Taylor, H. M. (1990). A First Course in Stochastic Processes (2nd ed.). Academic Press, New York.
Karlin, S. and Taylor , H.M. (1981). A Second Course in Stochastic Processes. Academic Press, N.Y.
Kijima, M. (1997). Markov Processes for Stochastic Modelling. Chapman Hall.
*Müller, D. (2007). Processos Estocásticos e Aplicações. Edições Almedina, Coimbra.
Ross, S. M. (1996). Stochastic Processes (2nd ed.) Wiley, New York.
Outra:
Breiman, L. (1992). Probability. SIAM , Philadelphia .
Brzezniak, Z. and Zastawniak, T. (1999). Basic Stochastic Processes. Springer.
Cox, D.R. and Miller, H.D. (1965). The Theory of Stochastic Processes. Chapman and Hall.
Doob, J. L. (1953, 1990). Stochastic Processes. Wiley, N.Y.
Grimmett, G. R. and Stirzaker, D. R. (1982, 2001). Probability and Random Processes. Oxford University Press.
Grimmett, G. R. and Stirzaker, D. R. (2001). One Thousand Exercises in Probability. Oxford University Press.
Kijima, M. (1997). Markov Processes for Stochastic Modelling. Chapman Hall.
Soong, T. T. (1973). Random Differential Equations in Science and Engineering. Academic Press.
