Measure Theory and Stochastic Processes

2021/2022

Prerequisite/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

Knowledge

  • 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

Skills

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

Competences

  • 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 137,5 hours for the student.

Exam

Exams

Name of examMeasure Theory and Stochastic Processes
Type of exam
Written or oral exam
ECTS5
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
SemesterAutumn
ECTS5
Language of instructionDanish and English
Location of the lectureCampus Aalborg
Responsible for the module

Organisation

Study BoardStudy Board of Mathematical Sciences
DepartmentDepartment of Mathematical Sciences
FacultyFaculty of Engineering and Science