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

Code	Subject	
MMC1011	Analysis of Stochastic Phenomena	

Section	Semester	Hours: C+S+L	Category	Type	
Computational Mathematics - in Hungarian	1	2+2+0		compulsory	
Computational Mathematics - in Hungarian	1	2+2+0	speciality	compulsory	
Didactic Mathematics - in Hungarian	1	2+2+0	speciality	compulsory	
Interdisciplinary Mathematics - in Hungarian	1	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Assoc.Prof. SOOS Anna, Ph.D., asoos@math.ubbcluj.ro	
Aims	The course gives the necessary knowledges for stochastic phenomena analysis.
After this lectures the students will be able to make abstract models for stochastic phenomena.   	
Content	1.Basic notions in probability theory
The notion of probability
Classical probability models
Random variables.
Numerical characteristics.
The laws of large numbers.
Probabilistic methods in natural sciences.
Probabilistic methods in social sciences
2. Stochastic processes
Markov chains.
Random walk.
Poisson processes.
Gaussian and nongaussian processes.
3. Statistics in natural sciences
Statistical estimates.
Statistical tests.
Random number generators.
Monte Carlo methods.
4. Times series
One dimensional times series.
ARMA series
Bilinear models.
In practices we use MATLAB.	
Bibliography	1. W. Feller: Bevezetés a valószínűségszámításba és alkalmazásaiba, Műszaki Kiadó, Budapest, 1992
2. S. Karlin: Sztochasztikus folyamatok, Tankönyvkiadó, Budapest, 1982
3. P. Michalberger, L. Szeidl, P. Varlaki: Alkalmazott folyamatstatisztika és idősor analízis, Typotex, 2001
4. M. Mitzenmacher, E. Upfal: Probability and Computing, Cambridge University Press, 2005  
5. A. Noga: The probabilistic method, Wiley,  2001
6. A. Soós:  A valószínűségszámítás elemei, Egyetemi Kiadó, Kolozsvár, 2001  
7. A. Soós:  A matematikai statisztika  elemei, Egyetemi Kiadó, Kolozsvár, 2005
	
Assessment	3 computer works: 30%
Analysis of a stochastic phenomenon-proiect: 70%