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Syllabus for

Academic year
TMS165 - Stochastic calculus - Part I
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0104 Project 5,0 c Grading: TH   5,0 c    

In programs

TM Teknisk matematik, Year 2 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)

Examiner:

Docent  Patrik Albin



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

Basic courses in mathematics and mathematical statistics at some technical, mathematical or statistically oriented university program.
To some extent, these prerequisites can be replaced by knowledge and/or interest for the applications mentioned above.

Aim

Calculus, including integration, differentiation, and differential equations are of basic importance for modelling in most branches of natural science.
However, these tools are insufficient to model a large number of phenomena which include "chance".
Examples of such phenomena are noise disturbance of signals in electrical engineering, uncertainty about future prices of stocks in economy, and the macroscopic result of many microscopic particle movements in biology or physics.
The tools required for this are stochastic analysis and stochastic differential equations.
The course gives a solid basic knowledge of stochastic analysis, including background material from calculus, probability theory and stochastic processes.

Content

Tools for calculus, probability theory, and stochastic processes that are required in stochastic calculus.
Brownian mottion calculus. Elements of Levy processes. Stochastic differential equations.
Applications in electrical engineering, mathematical finance, and biology. Numerical methods for stochastic differential equations.

Organisation

Lectures. Supervising of hand-ins and projects.

Literature

F.C. Klebaner: Introduction to Stochastic Calculus with Applications. Imperial Collage press.

Examination

Hand-ins and projects that are carried out in small groups.


Page manager Published: Thu 03 Nov 2022.