MC031 | Stochastic Processes and Fractals |
Teaching Staff in Charge |
Assoc.Prof. SOOS Anna, Ph.D., asoosmath.ubbcluj.ro |
Aims |
To give to the students the principal notions of the stochastic processes which are necessary in the model process of the economic, social and other fenomens. 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 |
Exam. |
Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |