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.,  hannemath.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
References
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%.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject