All basic directions and research themes have been developed and investigated on scientific project Stochastics and will be present in the next five years. In particular, following research areas are in the nearest focus.
For real second order stochastic process the conditional expectation is observed and treated as
nonlinear prediction. The mean square error for a Gausian case is treated using dynamics of Hermite polynomials. Also, the series of problems regarding summing of random number of independent random variables. The dependence of limiting distribution in terms of input distributions is investigated. This leads to some classes of infinitely divisible distributions and their properties. Stochastic analysis in Malliavin sense is used to precisely investigate distribution properties of stochastic differential equations.
Precisely, the connection with corresponding deterministic processes is established. Stochastic dynamic systems and the flows of projections are taken into account regarding Hilbert space techniques. The close relation between flows of algebras and orthogonal projections and spectral types is in constant focus of interest. Fuzzy sets and foundation of stochastic dynamics of such objects is very carefully studied and will be studied in the future. Fuzzy martingales with values in Banach spaces are an object of research interest, as well. The significance of seminars was greatly increased by the fact that they often served also as a substitute for graduate courses which, until recently, practically did not exist at the Universities in Serbia.