Measure Theory and Stochastic Processes


Recommended prerequisite for participation in the module

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.

Content, progress and pedagogy of the module

Learning objectives


  • 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


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


  • 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

Type of instruction

As described in §17 in the curriculum. 

Extent and expected workload

This is a 5 ECTS project module and the work load is expected to be 150 hours for the student.



Name of examMeasure Theory and Stochastic Processes
Type of exam
Written or oral exam
Permitted aidsDer henvises til den pågældende semesterbeskrivelse/modulbeskrivelse
AssessmentPassed/Not Passed
Type of gradingInternal examination
Criteria of assessmentThe criteria of assessment are stated in the Examination Policies and Procedures

Facts about the module

Danish titleMålteori og stokastiske processer
Module codeK-MAT1-MTSP
Module typeCourse
Duration1 semester
Language of instructionDanish and English
Location of the lectureCampus Aalborg
Responsible for the module


Study BoardStudy Board of Mathematical Sciences
DepartmentDepartment of Mathematical Sciences
FacultyThe Faculty of Engineering and Science