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Kursplan för

Läsår
TMS165 - Stokastisk analys - del I
 
Kursplanen fastställd 2011-02-22 av programansvarig (eller motsvarande)
Ägare: MPENM
7,5 Poäng
Betygskala: TH - Fem, Fyra, Tre, Underkänt
Utbildningsnivå: Avancerad nivå
Huvudområde: Matematik
Institution: 11 - MATEMATISKA VETENSKAPER


Undervisningsspråk: Engelska
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Blockschema: X

Modul   Poängfördelning   Tentamensdatum
Lp1 Lp2 Lp3 Lp4 Sommarkurs Ej Lp
0104 Tentamen 7,5hp Betygskala: TH   7,5hp   23 Okt 2012 fm V,  18 Jan 2013 fm V,  03 Apr 2013 fm V

I program

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Årskurs 1 (obligatoriskt valbar)

Examinator:

Docent  Patrik Albin


Kursutvärdering:

http://document.chalmers.se/doc/00000000-0000-0000-0000-000048F63D80


  Gå till kurshemsida

Behörighet:

För kurser inom Chalmers utbildningsprogram gäller samma behörighetskrav som till de(t) program kursen ingår i.

Kursspecifika förkunskaper

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.

Syfte

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.

Lärandemål (efter fullgjord kurs ska studenten kunna)

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

Innehåll

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, exercise sessions, supervising of home assignments.

Litteratur

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.


Sidansvarig Publicerad: on 24 jan 2018.