|
Special Topics in Computer Science:
Stochastic Processes and Fractals
| 339.011 |
1KV |
Soos |
Block |
Begin: 22.10.2008 |
During these lectures I will gives the basic notions of stochastic processes and fractal theory. As application we
will study the internet traffic as a fractional Brownian motion.
Lecturer
Dr. Anna Soos
Babes-Bolyai University, Cluj, Romania
asoos@cs.ubbcluj.ro
Dates
| Date |
Time |
Room |
| We 22.10.2008 |
15:30 - 18:00 |
J 311B
|
| Th 23.10.2008 |
15:30 - 18:00 |
K 223B
|
| Fr 24.10.2008 |
13:45 - 17:00 |
HF 9905
|
Contents
- Introductions
- Interated function system. Fractal sets and measures
- Fractal dimension
- Fractal functions
- Stochastic processes. Definitions, examples. Markov processes.
- Brownian motion. Generalizations: fractional, multifractional Brownian motion
- Internet traffic as fractional Brownian motion
Exam
The marks for this course will be based on a project.
Literature
- Falconer, K.J.: Fractal geometry, mathematical foundations and applications John Wiley & Sons, 1990.
- Hutchinson, J.E.: Fractals and Self Similarity, Indiana University Mathematics Journal, 30 (1981), no.5, 713-747.
- Kigami, J.: Analysis on fractals, Cambridge University Press, 2001.
- Mandelbrot, B.: The Fractal Geometrie of Nature, W.H. Freeman and Company, New York, 1977.
- Shyryaev A.: Probability, Springer, (1995)
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