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Course Catalog 1999/2000


Mathematics

MAM072 Random Processes 6.0 ECTS credits

TIMEPERIOD:


LANGUAGE:

EXAMINER
Astrid Hilbert Univ lekt


PREREQUISITES


COURSE AIM
Many physical or economic systems develop in time. This means that the current state of a system does depend on its history, and the future depends on the present state.
Stochastic processes are a mathematical tool for modelling the developement of a system in time.
In this course we will give a survey on/about different stichastic processes and the methods used to investigate them.
We will also show how the theoretical methods can be applied.

CONTENTS
1) Elements of probability theory and linear algebra.
a) A short repetition of basic techniques from these areas.
b) Processes
c) Stochastic Matrices

2) Markov-Chains
a) Markov property. Examples.
b) Properties of Markov chains
c) Stationary distribution
d) Asymtotic behavior
e) Applications

3) Markov Processes
a) Definition and comparison with chains
b) Properties: recurrence, transiens, mixing times(?)
c) Applications

4) Properties of specific Markov processes
a) Poison processes
b) Birth and death processes
c) Brownian motion
d) Ornstein Uhlenbeck processes

5) Second-order processes
a) Definition and basic properties
b) Orthoganal expansions
c) Spectral representation
d) White noise




TEACHING
The teaching consists of of lectures and computer exercises. Some lectures can be replaced by mandatory computer laborations.


EXAMINATION
A written examination at the end of the course.

COURSE GRADE SCALE:

ITEMS/CREDITS

Written exam 6.00ECTS

COURSE LITERATURE
Breiman, Leo: "Probability" Classics in applied mathematics 7, SIAM (Society for Industrial and Applied Mathematics), 1992
Iosifescu, Marius: "Finite Markov Processes and their Applications", John Wiley and Sons, 1979
Valid for the academic year 1999/2000.

Web Editor: Karin.Lindholm@dc.luth.se

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LULEÅ UNIVERSITY OF TECHNOLOGY
University Campus, Porsön, 971 87 Luleå. Tel. +46 (0) 920-91 000, fax +46 (0) 920-91 399
Last edited 1999-12-15