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Syllabus for

Academic year
TMS165 - Stochastic calculus 1  
 
Syllabus adopted 2013-02-21 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students
Block schedule: X

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0104 Examination 7,5c Grading: TH   7,5c   22 Oct 2013 am V,  17 Jan 2014 pm V,  23 Apr 2014 am V  

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)

Examiner:

Docent  Patrik Albin


Course evaluation:

http://document.chalmers.se/doc/4662709c-7a98-45bf-bd34-4271d52edc33


  Go to Course Homepage

Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

An undergraduate course in mathematical statistics.
Students with a strong mathematical background do not need a mathematical statistical background, as might not graduate students from other fields in science - please contact the examiner for advice.

Aim

Calculus, including integration, differentiation, and differential equations are of fun-
damental importance for modelling in most branches on natural sciences. However,
these tools are insufficient to model a large number of phenomena which include
"chance" or "uncertainty". Examples of such phenomena are noise disturbances of
signals in engineering, uncertainty about future stock prices in finance, and the
macroscopic result of many microscopic particle movements in natural sciences.
Among the most important tools required for the modelling of the latter phenomena
are stochastic analysis and stochastic differential equations. The course gives a solid
basic knowledge of stochastic analysis and stochastic differential equations, including
background material from calculus, probability theory and stochastic processes.

Learning outcomes (after completion of the course the student should be able to)

Use stochastic analysis and stochastic differential equations as professional tools for engineering and natural science phenomena including "chance" and "uncertainty".

Content

Tools from calculus, probability theory and stochastic processes that are required in stochastic calculus. Brownian motion calculus. Elements of Levy processes and martingales. Stochastic integrals. Stochastic differetial equations. Examples of applications in engineering, mathematical finance and natural sciences. Numerical methods for stochastic differential equations.

Organisation

Lectures and supervised work with esexercises.

Literature

Fima C. Klebaner (2005). Introduction to Stochastic Calculus with Applications, 2nd Edition, Imperial College Press, London, selection of material from Chapters 1-6 and 10. Additional lecture notes on numerical methods.

Examination

Written exam.


Published: Mon 28 Nov 2016.