Forudsætninger/Anbefalede forudsætninger for at deltage i modulet

The module builds on knowledge obtained by the modules Linear Algebra with Applications, Analysis 1, Analysis 2, and Probability Theory from the BSc in Mathematics-Economics.

Modulets indhold, forløb og pædagogik

Læringsmål

Viden

• know selected topics concerning general measure theory with special focus on probability theoretical. Topics as existence and uniqueness of measures, Lebesgue-integration, Expectation and condition expectation, Radon-Nikodyms theorem, and information expressed through sigma-algebras
• know about stochastic processes in discrete and continuous time
• know about  Wiener  processes
• know about Martingales
• know about stochastic integrals, Ito’s formula and Girsanovs theorem

Færdigheder

• are able to calculate fundamental characteristics for stochastic processes.
• are able to conduct a change of measure for a martingale

Kompetencer

• are able to formulate mathematical results in a correct manner by means of measure-theoretical and probabilistic argumentation.
• are able to apply and mediate basic mathematics and theory related to stochastic processes.
• able to gain additional knowledge regarding probability theoretical subjects related to stochastic processes and their application in Finance

Undervisningsform

As described in the introduction to Chapter 3.

Omfang og forventet arbejdsindsats

Kursusmodulets omfang er 5 ECTS svarende til 150 timers studieindsats.
 

Eksamen

Prøver

Prøvens navn	Measure Theory and Stochastic Processes
Prøveform	Skriftlig eller mundtlig
ECTS	5
Bedømmelsesform	Bestået/ikke bestået
Censur	Intern prøve
Vurderingskriterier	Som angivet i Fællesbestemmelser for uddannelser: http:/​/​www.engineering.aau.dk/​uddannelse/​Studieadministration/​