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Syllabus:

# Stochastic Processes and Simulation, 7.5 Credits

Swedish name: Stokastiska processer och simulering

This syllabus is valid: 2015-08-24 and until further notice

Course code: 5MS049

Credit points: 7.5

Education level: First cycle

Main Field of Study and progress level: Mathematical Statistics: First cycle, has less than 60 credits in first-cycle course/s as entry requirements

Responsible department: Department of Mathematics and Mathematical Statistics

Established by: Faculty Board of Science and Technology, 2015-06-11

## Contents

Moment 1 (4.0 hp): Theory. Moment covers the basic theory of stochastic processes theory of stochastic simulation (Monte Carlo methods). The course covers the generation of random numbers from diﬀerent continuous and discrete distributions and integral estimation including error estimation. Further, theory and methods for simulating random walks, Brownian motion, Poisson processes and Markov chains are introduced together with their real life applications.

Moment 2 (3.5 hp): Computer labs. Application of the introduced computer intensive methods using suitable programming language. Additionally the simulation of queuing and production lines and inventory systems based on the discrete events approach is introduced.

## Expected learning outcomes

Expected learning outcomes

• Determine algorithms for simulating random numbers from the discrete and continuous distributions
• Use simulatioons to estimate integrals and properties of random variables together with corresponding measures of accuracy
• Calculate analytically the properties of random walk, Brownian motion, Poisson process and Markov Chains
• With help of computer software, simulate the realisations of the stochastic processes introduced in the course and use them to estimate properties of the underlying random processes
• Construct simple discrete event based systems and analyse their output
• Present the results of the analysis in oral and written form.

## Required Knowledge

The course requires 15 ECTS mathematics,  6 ECTS mathematical statistics and 7.5 ECTS computer programming, or equivalent. Proficiency in English equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.

## Form of instruction

Lectures, classes and computer labs

## Examination modes

Written examination on moment 1 (U/3,4,5) Written lab reports and oral presentation on moment 2 (U/G)