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Regular version of the site
2016/2017

## Research Seminar "Probability Theory. Analytical and Economic Applications 1"

Type: Optional course (faculty)
When: 1, 2 module
Language: English
ECTS credits: 3

### Course Syllabus

#### Abstract

In this course we discuss various topics of modern probability theory, stochastic processes, and statistics. Special emphasis is given to probabilistic problems with strong analytic aspects and problems with applications in economy. Pre-requisites : Theory of Probability, Functional Analysis, Partial Differential Equations Course Type: elective #### Learning Objectives

• Acquire a familiarity with random processes used in economic models, in models of financial mathematics, and to use them for making predictions. Study of stochastic analysis, and of analytic methods in the theory of random variables. #### Expected Learning Outcomes

• The students will be expected to have an understanding of theoretical principles necessary for the construction of models used in economics. They should be able to apply methods of modern stochastic analysis, and of analytical methods from the theory of probability to the study of economics models #### Course Contents

• Measures on infinite dimensional spaces. Equivalence and singularity, Gaussian measure. Kolmogorov Theorem. Weak convergence and Prokhorov’s Theorem. Isoperimetric inequality, Sobolev inequality. Sobolev space. Convexity
• Wiener processes. Stochastic integral, and Ito’s formula. Stochastic differential equations. Ornstein-Uhlenbeck process #### Assessment Elements

• Task
• Final exam #### Interim Assessment

• Interim assessment (2 module)
0.7 * Final exam + 0.3 * Task #### Recommended Core Bibliography

• Statistics for business and economics, Newbold, P., Carlson, W. L., 2007

#### Recommended Additional Bibliography

• A. Ya. Dorogovtsev, D. S. Silvestrov, A. V. Skorokhod, & M. I. Yadrenko. (2018). Probability Theory: Collection of Problems. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1790324