Subject: Stochastic Processes	Code: MC401	

Semester	 Hours: C+S+L	Type	 Section	
1	2+2+0	compulsory	Optimization of computational models- in Hungarian	

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. Applications in Operations Research: The theory of queues. Single server queueing models. Multiple server queueing models. Queues with a finite population.
4. Reneval processes. Renewal functions. Limit theorems	
Selective References	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. Iosifescu, M., Grigorescu, S., Oprisan, Gh., Popescu, Gh., Elemente de modelare stochastica, Ed. Tehnica, Bucuresti, 1971.
4. Karlin, S., A first cours in stochastic processes, Academic Press, New York and London, 1966
5. Mihoc, Gh., Bergthaller, C., Ursianu, V., Procese stochastice, Ed.Stiintifica si Enciclopedica, Bucuresti, 1978	
Assessment	Exam