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

Code	Subject	
MMC1006	Stochastic Processes and Applications	

Section	Semester	Hours: C+S+L	Category	Type	
Applied Mathematics	4	2+2+0	speciality	optional	

Teaching Staff in Charge	Assoc.Prof. LISEI Hannelore-Inge, Ph.D., hanne@math.ubbcluj.ro	
Aims	The aim of this course is to provide basic concepts and tools about stochastic processes and stochastic integration, to elaborate stochastic models with applications in economy, population dynamics etc.  	
Content	1. Stochastic processes
2. Brownian motion
3. Martingales
4. Stochastic integrals and Ito formula
5. Stochastic differential equations 
6. Simulation of stochastic processes
7. Applications of stochastic processes
	
Bibliography	1) Blaga P., Calculul probabilităţilor şi statistică matematică. Vol. II. Curs şi culegere de probleme, UBB, Cluj-Napoca, 1994.
2) Ciucu G., Tudor C., Probabilităţi şi Procese Stocastice. Vol.I, Vol.II., Edit. Acad. 1978, 1979.
3) Florea D., Tudor C., Procese Stocastice. Probleme şi Soluţii. Edit. Univ. Bucureşti, 1982. 
4) Iftimie B., Tudor C., Tudor M., Procese Stocastice cu Aplicaţii in Finanţe. Edit. Acad. de Studii Economice, Bucureşti, 1998 
5) Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus, Springer Verlag, New York, 2005. 
6) Lisei H., Probability Theory, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2004. 
7) Lisei H., Micula S., Soós A., Probability Theory through Problems and Applications,  University Press, Cluj-Napoca, 2006. 
8) Kloeden P., Platen E., Numerical Solution of Stochastic Differential Equations, Springer Verlag, 1995.
9)  Mikosch Th., Elementary Stochastic Calculus with Finance View, World Scientific, Singapore, 1998. 
10) Oksendal B., Stochastic Differential Equations, Springer Verlag, 2003.
	
Assessment	The final grade is computed as follows: written exam at the end of the semester  50%; activity during the semester: 25%; presentation of a report: 25%.