# FIM3010 Stochastic Methods 5.0 credits

#### Stokastiska metoder

Contents

Random numbers, optimization methods, Markov processes, Monte Carlo methods and stochastic calculus and differential equations, survey of real world examples of stochastic methods.

Course objectives

When you have finished the course, you are required to show the following skill:

List examples of different stochastic methods and judge when the methods are applicable.

Explain the physical principles and background of Monte Carlo methods and stochastic calculus.

Illustrate and discuss how Monte Carlo methods are constructed.

Learning outcomes

When you have finished the course, you are able to:

List examples of different stochastic methods and judge when the methods are applicable.

Explain the physical principles and background of Monte Carlo methods and stochastic calculus.

Illustrate and discuss how Monte Carlo methods are constructed.

Course schedule

1 week pre-study exercises

1 week lectures and hands-on compuer exercises

1 week project assignment

Course part of the national e-Science research school SeSE (www.sese.nu)

### Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

## Course information

### Content and learning outcomes

#### Course contents *

Random numbers, optimization methods, Markov processes, Monte Carlo methods and stochastic calculus and differential equations, survey of real world examples of stochastic methods.

#### Intended learning outcomes *

When you have finished the course, you are able to:

List examples of different stochastic methods and judge when the methods are applicable.

Explain the physical principles and background of Monte Carlo methods and stochastic calculus.

Illustrate and discuss how Monte Carlo methods are constructed.

#### Course Disposition

3 weeks format in line with the SeSE course format

1 week pre-study

1 week lectures and hands-on computer exercises

1 week project assignment

### Literature and preparations

#### Specific prerequisites *

Ph. D students in computational sciences and e-science

Basic knowledge in statistics and probability theory and basic knowledge using Matlab/Octave.

#### Recommended prerequisites

Basic knowledge in statistics and probability theory and basic knowledge using Matlab/Octave.

#### Equipment

Laptop with Matlab (or Octave) installed.

#### Literature

C. Gardiner, Stochastic Methods- A handbook for the Natural and Social Sciences , Springer Verlag 2009, ISBN: 978-3-540-70712-7

J. C. Spall, Introduction to Stochastic Search and Optimization, Wiley 2003, ISBN: 978-0-471-33052-3

N. G. van Kampen, Stochastic Processes in Physics and Chemistry, Elsevier, ISBN:978-0-444-52965-7

### Examination and completion

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#### Examination *

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Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

#### Other requirements for final grade *

Examination (pass/fail):

Passing computer exercises

Project work with oral and written presentation

#### Opportunity to complete the requirements via supplementary examination

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#### Opportunity to raise an approved grade via renewed examination

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### Further information

#### Course web

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#### Offered by

SCI/Applied Physics

#### Main field of study *

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#### Education cycle *

Third cycle

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#### Contact

Lars Bergqvist (lbergqv@kth.se)

#### Ethical approach *

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.