Stochastic Differential Equations
Code
11635
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Oleksiy Karlovych
Teaching language
Português
Objectives
At the end of this course students will have acquired basic knowledge and skills in the area of stochastic differential equations in order to:
- Understand advanced contents in the area;
- Being able to start a research work in the area.
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 - Feynman-Kac Formula
Bibliography
A. Friedman, Stochastic Differential Equations and Applications, volume 1, Academic Press 1975.
Hui Hsiung Kuo, Introduction to Stochastic Integration, Springer, 2006.
P. Malliavin, Integration and Probability, Springer, 1995.