Research Seminar "Probability Theory. Analytical and Economic Applications 1"
- 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.
- 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
- 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
- Statistics for business and economics, Newbold, P., Carlson, W. L., 2007
- 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