Syllabus for |
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TMS165 - Stochastic calculus
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| Syllabus adopted 2014-02-17 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:
| Course module |
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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 |
7,5 c |
Grading: TH |
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7,5 c
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27 Oct 2015 am V, |
04 Jan 2016 pm M, |
19 Aug 2016 am SB
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In programs
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
Examiner:
Docent
Patrik Albin
Go to Course Homepage
Eligibility:
In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement:
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.
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 fundamental 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 calculus as a professional tool in applications to engineering sciences and natural sciences
Content
Tools from calculus, probability theory and stochastic processes that are required in stochastic calculus. Brownian motion calculus. Elements of Markov processes and martingales. Stochastic integrals. Stochastic differetial equations and diffusion processes. Change of probability measure and Girsanov transformation. Examples of applications. Numerical methods for stochastic differential equations.
Organisation
Lectures and exercise sessions.
Literature
Chapters 1-6 and 10 in "Fima C. Klebaner (2012). Introduction to Stochastic Calculus with Applications, Third Edition, Imperial College Press, London". Additional lecture notes on applications and numerical methods.
Examination
Written exam.