Stochastic differential equations (2013/2014)

Course code
4S001444
Name of lecturer
Laura Maria Morato
Coordinator
Laura Maria Morato
Number of ECTS credits allocated
6
Academic sector
MAT/06 - PROBABILITY AND STATISTICS
Language of instruction
English
Location
VERONA
Period
II semestre dal Mar 3, 2014 al Jun 13, 2014.

Lesson timetable

Learning outcomes

In this course we will introduce the audience to the basic elements of Ito non anticipative stochastic calculus and Stochastic Differential Equations.

Synthetic programme : Brownian Motion, Martingales, Ito integral, Ito formula and martingale representation theorem, strong and weak solutions of a stochastic differential equation, diffusion theory, Feynman Kac formula, application to filtering and stochastic control theory.

Syllabus

Detailed Programme

- Probabilty spaces, random variables, stochastic processes and martingales

- Brownian motion

- Ito integral: construction, properties and extensions

- Ito formula and Martingale representation theorem

- Stochastic differential equations: examples of solution, existence and uniqueness of strong solution, weak solutions, Girsanov theorem and Cameron-Martin formula.

- Diffusion theory : Markov property, generators.

- PDEs problems associated to a diffusion : Dirichlet problem, Parabolic equations, Feynman-Kac formula.

- Application to filtering and stochastic control theory

Assessment methods and criteria

Discussion of home works.