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 | Active participation/continuous evaluation
Re-exam: 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 |