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

Code	Subject	
MC265	Stochastic Processes	

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

Teaching Staff in Charge	Assoc.Prof. SOOS Anna, Ph.D., asoos@math.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 fenomens.	
Content	1. Stochastic processes discrete in space and time. Markov chains. Transition probability matrices of a Markov chain. Chapman-Kolmogorov equation. The homogeneous Markov chain. Classification of states. The ergodic Markov chain.
2. Stochastic processes discrete in space and continuous in time. The homogeneous Markov process. The Poisson process. The simple birth process. The simple death process. The simple birth- and- death process. 
3. Wiener processes. Properties and quadratic variation. Brownian motion.
4. Martingale and semimartingale.
5. Stochastic integral Ito formula for Wiener processes and fractional Wiener processes.
6. Stochastic differential equations. Different type of equations. Numerical solutions.
7. Applications.	
Bibliography	1. Bharucha-Reid, A.T., Elements of the Theory of Markov Processes and their Applications, McGraw-Hill Book Company, Inc, Now York. Toronto. London, 1960.
2. Iosifescu, M., Lanturi Markov finite si aplicatii, Ed. Tehnica, Bucuresti, 1977.
3. Karlin, S., A first cours in stochastic processes, Academic Press, New York and London, 1966
5. Medvegyev P.: Sztochasztikus analizis, Typotex, Budapest, 2004
4. Michalberger,  P., Szeidl, L., Varlaki, P.: Alkalmazott folyamatstatisztika es idoszor-analizis, Typotex, 2001
5. Oksendhal, S.: Stochastic differential equations, Springer, 2001
6. Tusnady, G., Ziermann, M. Idosorok analizise,  Muszaki Kiado, Budapest, 1986	
Assessment	Exam.