(Created 2010-07-25.)

PROBABILITY THEORY | FMSF05 |

**Aim**

The course gives a deaper and extended knowledge of probability theory, useful for further studies in, e.g., extreme value theory and stochastic processes and their applications.

*Knowledge and understanding*

For a passing grade the student must

- be able to explain different concepts in stochastic convergence and how they relate to each other,
- be able to explain the concepts of characteristic and moment generating functions and how these functions can be used,
- be able to descibe the multi dimensional normal distribution and the invariance properties under, e.g., linear combinations and conditioning,
- be able to explain the definition and basic properties of the Poisson process.

*Skills and abilities*

For a passing grade the student must

- show the ability to integrate knowledge from the different parts of the course when solving problems.

**Contents**

The course deapens and expands the basic knowledge in probability theory. Central moments in the course are transforms of distribution, conditional expectations, multidimensional normal distribution, and stochastic convergence. Further, the concept of stochastic processes is introduced by a fairly thourough treatment of the properties of the Poisson process.

**Literature**

Gut, A.: An Intermediate Course in Probability Theory. Springer 1995.