Stochastic Differential Equations
Code
8540
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Maria Fernanda de Almeida Cipriano Salvador Marques
Weekly hours
2
Teaching language
Português
Subject matter
1-Brownian Motion- Wiener integral- Conditional expectation- Martingales
2-Stochastic integrals
3-Itô formula
4- Applications of the Itô Formula- Exponential process- Transformation of probability measures-Girsanov theorem
5- Stochastic Differential equations-Existence and uniqueness-Markov property-Diffusion processes- Semigroups and Kolmogorov equations
6-Linear stochastic differential equations- Applications to Finance- Feynman-Kac Formula
Bibliography
1 -- Hui.Hsiung Kuo: Introduction to Stochastic Integration. Springer. 2006
2 -- Bernt Oksendal: Stochastic Differential Equations. Sringer. 1998
3 -- Paul Malliavin: Integration and Probability. Springer-Verlag. 1995
Evaluation method
1 – Frequency
is assigned to students who have attended at least two thirds of the lessons taught.
2 - Evaluations
Only students who have frequency, special or are working students can participate in the evaluations.
Evaluations are done through continuous evaluation and examination of Appeal.
2.1 Continuous evaluation
consist in three elements of T1, T2 and T3.
Each element consist in the resolution of a list of exercises outside the classroom, and an oral presentation of a part of the theoretical matter, previously established by the teacher.
Each element (T1, T2, T3) has the classification of 20 points.
Classification of continuous evaluation is achieved by making the arithmetic average of the marks obtained in T1, T2 and T3.
If the classification of continuous evaluation is greater than or equal to 9.5, the student is approved with this classification rounded to unities. if the classification of continuous is less than or equal to 9.4, the student may be referred to the Appeal.
2.2 - Examination of Appeal
They may be the examination of Appeal all students enrolled in the course who have obtained frequency or have a special status. If the test classification is greater than or equal to 9.5, the student is approved for this classification rounded unities. If the test classification is less than 9.4, the student is not approved.