Syllabus for |
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TMS165 - Stochastic calculus 1
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| Syllabus adopted 2013-02-21 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits |
| Grading: TH - Five, Four, Three, Not passed |
| Education cycle: Second-cycle |
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Major subject: Mathematics |
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: English
Open for exchange students
Block schedule:
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0104 |
Examination |
7,5c |
Grading: TH |
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7,5c
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22 Oct 2013 am V, |
17 Jan 2014 pm V, |
23 Apr 2014 am V
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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.