Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Large deviations principles (17.D0M51L)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Year: 1, Semester: Summer)

General information:

Category	Professional-applicative
Scientific or art field	Teorijska i primenjena matematika
ECTS	10

The objective of the course is to acquire basic knowledge in the field of large deviations principle. Student should be able to apply the acquired knowledge from the field of large deviations principle in in image processing, statistical mechanics, encoding theory.

Student should acquire basic knowledge from the large deviation theory and the large deviations of processes on three levels. The students can use the acquired knowledge in engineering subjects and in practice, to develop and solve mathematical models using the knowledge of large deviations theory.

The course content includes the following topics. 1) Probability theory 2) Stochastic processes 3) Definition of large deviations principles 4) Large deviation principle for stochastic process 5) Some applications of large deviations principles

Lectures. Consultations. The lectures are organized in combined form. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. In addition to lectures there are regular consultations. A students writes a seminar paper in the filed of application of large deviation theory in the field of their scientific interest and gives an oral presentation related to it. Through study and research work a student works independently on getting deeper understanding of the subject matter through study of the scientific journals and other relevant literature. Working with the course teacher, the students are prepared for independent work on writing a scientific paper.

Authors	Title	Year	Publisher	Language
Billingslay, P.	Probability and Measure	1986	John Wiley & Sons, New York	English
A. Dembo, O. Zeitouni,	Large Deviation Techniques and Applications	1988	Springer	English
J. Feng, T.G.Kurtz	Large Deviation for Stohastic Processes	2006	American Mathematical Society	English