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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

  1. Introductions
  2. Interated function system. Fractal sets and measures
  3. Fractal dimension
  4. Fractal functions
  5. Stochastic processes. Definitions, examples. Markov processes.
  6. Brownian motion. Generalizations: fractional, multifractional Brownian motion
  7. 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)