Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate

SUBJECT

Code
Subject
MMP0004 Stochastic Processes and Fractals
Section
Semester
Hours: C+S+L
Category
Type
Mathematics - in Hungarian
6
2+0+1
speciality
optional
Computer Science - in Hungarian
Computer Science - in Hungarian, Miercurea Ciuc
6
2+0+1
speciality
optional
Information engineering
8
2+0+2
speciality
optional
Teaching Staff in Charge
Assoc.Prof. SOOS Anna, Ph.D.,  asoosmath.ubbcluj.ro
Aims
To give to the students the basic notions of the stochastic processes which are necessary in the model process of the economic, social and other phenomena. To introduce the basic notions of fractal theory.
Content
1. Stochastic processes: definitions and classification. Markoc chane. Transition probabilities. Chapman Kolmogorov relations. Random walk.
2. Continue Stochastic processes. Markov type processes. Poisson processes. Gaussian processes.
3. Contraction principle. Iterated function systems.
4. Hausdorff measure. Definition and properties.
5. Hausdorff dimension. Definition and properties.
6. Invariant sets, fractal sets. Existence and uniqueness.
7. Invariant measure, fractal measure.
8. Fractal functions. Fractal interpolation.
9. Selfsimilariry.
10. Similarity dimension.
11. Stochastic fractals.
12. Applications: Brownian motion. Fractal compression. Virtual reality.
References
1. M.F.BARNSLEY: Fractals Everywhere, Academic Press,1993.
2. K.J.FALCONER: Fractal geometry, mathematical foundations and applications, John Wiley & Sons, 1990.
3. K.J.FALCONER: Techniques in fractal geometry, John Wiley & Sons, 1997.
4. S. KARLIN, H. TAYLOR: A First Course in Stochastic Processes, Academic Press, 1975.
5. A. SOOS: Contraction Methods in Fractal Theory, Cluj University Press
Printing House, 2002.
Assessment
Practical works 30%
Presentation 30%
Exam 40%
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject