Scientific schools – Department of Probability Theory, Statistics and Actuarial Mathematics

Scientific School of Probability Theory and Mathematical Statistics” (founded in 1949 by academician of the Academy of Sciences of the Ukrainian SSR B.V. Gnedenko)
“Scientific School of Actuarial and Financial Mathematics” (founded in 1993 by M.Y. Yadrenko, Corresponding Member of the National Academy of Sciences of Ukraine)

Fields Of Scientific Research

Theory of stochastic processes, stochastic analysis and stochastic differential equations:

Fractional processes, fractional stochastic analysis. Stochastic calculus of fractional and multifractional processes and fields. Stochastic differential equations containing fractional Brownian motion. Approximation of solutions of stochastic differential equations. Stochastic differential equations with partial derivatives and fractional noises (Y.S. Mishura, K.V. Ralchenko);
Random processes from Orlicz spaces, sub-Gaussian and -sub-Gaussian random processes. Exponential estimates of distributions of extremum functionals (R.E. Yamnenko);
Approximation of random processes in different functional spaces (T.O. Yanevych);
Correlation and spectral theory of random fields; study of random fields associated with partial differential equations with random initial conditions; processes with random time change (L.M. Sakhno);
Stochastic differential equations with Levy noise. Levy-type processes and related integro-differential equations (V.P. Knopova)
Analysis of homogeneous and inhomogeneous perturbed Markov chains and processes; stability and ergodic theory. Renewal theory for heterogeneous Markov chains. Using the coupling method for stability analysis. (V.V. Golomoziy);
Studying asymptotic behavior of stochastic models of population dynamics, stochastic SIR models, which are described by the systems of stochastic differential equations with jumps (O.D. Borysenko);
Stochastic differential equations with partial derivatives and with general stochastic measures (I.M. Bodnarchuk).

Statistics of random processes and fields, applied statistics:

Statistics of heterogeneous random fields and processes, hidden Markov chains, models with variable noise intensity. Non-parametric analysis of mixtures with variable concentration . Statistics of heterogeneous data, in particular, change point detection. Nonparametric statistics based on the model of mixture and mixture with variable concentrations – estimation of distribution and density, hypothesis testing, classification. Psychometrics, statistical analysis of Kelly grids (R.E. Maiboroda);
Parametric estimation in the models with long-range dependence (Y.S. Mishura, K.V. Ralchenko, S.V. Shklyar);
Parametric and non-parametric estimation of stationary processes and fields in the spectral domain (L.M. Sakhno);
Regression models with errors in variables (S.V. Shklyar);
Survey sampling; analysis of statistical data; criteria for testing hypotheses about the correlation function of random processes (T.O. Yanevych);
Оптимізація алгоритмів комп’ютерної статистики (R.E. Yamnenko).

Stochastic dynamic systems:

Limit theorems of probability theory:

Functional limit theorems in application to financial models (Y.S. Mishura);
Limit theorems for functionals of random fields and statistical applications (L.M. Sakhno);
Limit theorems for solutions of stochastic differential equations and their application to partial differential equations (O. D. Borysenko).

Financial mathematics:

Stochastic models with long-range dependence. Fundamental properties of financial models. Study of models with stochastic volatility (Y.S. Mishura).

Risk theory and actuarial mathematics:

Solvency models and risk management systems of insurance company (V.P. Zubchenko);
Application of results on the ergodicity and stability of Markov processes to the construction of stochastic models of risk processes and processes in actuarial mathematics (V.V. Golomoziy);
Estimation of ruin probability for risk processes from Orlicz spaces of exponential type (R.E. Yamnenko).