In the project are investigated the fundamental issues of mathematical statistics in particular kernel estimates and the fundamental issues of stochastic analysis. In particular, the Bernoulli regression function is studied, a Nadaraya-Watson kernel type estimate is constructed. The limit distribution of the constructed estimate is investigated. The integral square deviation of the constructed estimate is found. Based on constructed estimate the new tests are constructed for the hypothesis testing. The properties of the constructed hypotheses are studied, they compared with other known hypotheses. Various approaches are proposed for the constructive representation of the stochastic structural design of ito-stochastically smooth Brownian functionals. The basic problems of the mathematics of stochastic results are obtained, in particular to solve the problems of exotic optional pricing.

Project members:

• Grigol Sokhadze (Principal Investigator)

• Omar Purtukhia (Coordinator)

• Elizbar Nadaraya (Key Personnel)