# Stochastic Processes and Simulation II, 7.5 ECTS

First level## Facts

No available facts**Course code**MT5004

## Syllabus

## Description

The two important parts of the course are the Renewal theory and the theory of Brownian motion.

Renewal Theory: One of the most unrealistic assumptions you receive during the basic courses is that the stochastic processes are memoryless (Markovian, as it is called). In the Renewal Theory we gave goodbye to Markov, and study the processes where the future advancement is not linked to the past. Therefore we lose some of the simplicity and elegance, but instead receive significantly more realistic results.

Brownian Motion: When a particle moves randomly, (like, for instance, a molecule in gas), its movement can often be seen as a sum of a large amount of impulses (collisions with other molecules in the gas). Due to the fact that the sums of stochastic variables are normally distributed the particles movements should during a certain time be normally distributed. If we assume that the time perspective which interests us is a lot larger then the interval between two impulses, we can pull out the normally distributed assumption to its outer consequence, and assume that the particles movement under as short of a period as we wish is normally distributed. Then the particle describes Brownian motion. This mathematical model has come to use not only within physics but also in many other areas within science and economy.

## Area of interests: Science and Mathematics

Science and mathematics help us understand how the world around us is connected – from the origin and structure of the universe, to the development and function of humanity and all other organisms on earth. Scientific knowledge makes it possible to critically examine the credibility of information in different areas of everyday life, society, and the media. As a scientist or mathematician, you will be attractive on a large job market that covers all parts of society and includes everything from pure technology companies to environment and healthcare, as well as research.

## Subject

### Mathematical Statistics

Mathematical statistics is the subject within applied mathematics that describes and analyses random events.

The foundation is the mathematical probability theory, which goes back to the 17th century, but has in its modern form developed mostly during the 20th century. Probability theory is also the foundation of statistical theory on how to draw conclusions from data with random features. The rise of computer technology has also significantly contributed to broadening the field of applications within mathematical statistics. Today is mathematical statistics one of the most powerful tools in applied mathematics.

Examples that apply mathematical statistics to a large extent are the insurance and finance sectors, biological and medical research (biostatistics) and industrial applications like telecommunications and quality control.

The department cooperates closely both in research and teaching with the pharmaceutical industry, medical institutions and banking and insurance companies. Depending on direction of studies, a student with an exam in mathematical statistics has a good chance to get employment in these sectors.

Mathematical statistics can be studied in elective courses, as a major in a Bachelor’s or Master’s degree or as a complementary subject. Courses cover both theory and applications in various areas. Mathematical statistics is included in the Bachelor’s programmes in Mathematics, Biomathematics and Mathematics and Economics and a major in the Master’s programmes in Mathematical statistics, Biostatistics, Finance mathematics and Finance and Actuarial science.