Recommended prerequisite for participation in the module

The module builds on knowledge and skills obtained in Linear Algebra with Applications, Mathematical Analysis 1 & 2 as well as Integration Theory and Hilbert Spaces. Knowledge acquired in Probability Theory will be helpful.

Content, progress and pedagogy of the module

Learning objectives

Knowledge

• Know about applications of general measure and integration theory to probability theory, in particular, the concept of independence and its relation to convolution semigroups of probability measures
• Know about the construction, interpretation, and usage of conditional expectations
• Know about stochastic processes in discrete and continuous time
• Know about processes with independent and stationary increments, in particular, standard Brownian motions
• Know about standard filtered probability spaces, adapted and progressive processes as well as stopping times
• Know basic theorems about martingales as well as continuous local martingales and their quadratic variations

Skills

• Are able to apply computation rules and calculi associated with the notions of independence and conditional expectations
• Are able to do computations with and understand proofs involving stochastic processes, in particular, those having independent and stationary increments
• Are able to perform calculations and argumentations involving stopping times
• Are able to apply basic results on martingales and continuous local martingales

Competences

• Are able to read, understand, criticize and make use of advanced literature on probability theory and stochastic analysis
• Are able to mediate basic theory of stochastic processes and apply it, for instance to financial mathematics

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.

Exam

Exams

Name of exam	Stochastic Analysis
Type of exam	Written or oral exam
ECTS	5
Permitted aids	Der henvises til den pågældende semesterbeskrivelse/modulbeskrivelse
Assessment	Passed/Not Passed
Type of grading	Internal examination
Criteria of assessment	The criteria of assessment are stated in the Examination Policies and Procedures