FIELDS OF SCIENTIFIC RESEARCH
Team of the research "Evolution systems: analytical transformation research, random fluctuations and statistical regularities"
Scientific research at the Department of Probability, Statistics and Actuarial Mathematics is developed at the following main areas:
Theory of stochastic processes, stochastic analysis and stochastic differential equations:
Statistics of stochastic processes and random fields. Applied statistics:
- Martingales and related processes, stochastic integration (Yu. Mishura);
- Spaces of random variables and φ-sub-Gaussian random processes (Yu. Kozachenko, O. Vasylyk, R. Yamnenko);
- Orlicz spaces and random processes from Orlicz spaces. Properties of queues formed by such processes. Accuracy and reliability of Monte-Carlo method, with applications (Yu. Kozachenko, R. Yamnenko);
- Wavelet expansions of random processes: existence and convergence rate in some norms; existence and the rate of convergence of expansions of random processes into the series with uncorrelated terms generated by wavelets (Yu. Kozachenko);
- Approximation of random processes in functional spaces (Yu. Kozachenko, T. Yanevich);
- Approximations of solutions to stochastic differential equations (Yu.Mishura, G. Shevchenko, K. Ralchenko);
- Correlation and spectral theory of random fields (O. Ponomarenko, L. Sakhno);
- Analysis of time-homogeneous and inhomogeneousely perturbed Markov chains and processes: stability and ergodic theory (M.Kartashov, V. Golomosiy);
- Stochastic calculus of fractional and multifractional processes and fields. Stochastic differential equations involving fractional Brownian motion (Yu. Mishura, G. Shevchenko, K. Ralchenko);
- Local times and occupation measures (G. Shevchenko).
Stochastic dynamic systems investigations:
- Methods of majorizing measures in the theory of random processes and in statistics of random processes (Yu. Kozachenko);
- Statistics of non-homogeneous random fields and stochastic processes, hidden Markov chain models, models with varying noise intensities (R. Maiboroda);
- Nonparametric analysis of mixtures with varying concentrations (R. Maiboroda);
- Statistics of non-homogeneous data, including change-point detection (R. Maiboroda);
- Nonparametric statistics of finite mixture models and mixtures with varying concentrations - distribution and density estimation, hypotheses testing, classification (R. Maiboroda);
- Psychometrics: statistics of Kelly grids (R. Maiboroda);
- Parameter estimation in the models with long-range dependence (Y. Mishura);
- Parametric and nonparametric estimation of stationary processes and fields in the spectral domain (L. Sakhno);
- Regression models with errors in variables (S. Shklyar).
Limit theorems in probability theory:
- Partial differential equations with random factors: conditions of existence of solutions, distribution of functionals of solutions, approximation and simulation of solutions (Yu. Kozachenko);
- Minimax methods of extrapolation, interpolation and filtering of stochastic processes and random fields (M. Moklyachuk);
- Computer simulation of random processes and fields (Yu. Kozachenko, O. Vasylyk);
- Random oscillating systems (O. Borysenko).
Risk theory and actuarial mathematics:
- Functional limit theorems for random fields (Yu. Mishura);
- Limit theorems for solutions of stochastic differential equations and applications to the partial differential equations (O. Borysenko, V. Zubchenko);
- Limit theorems for functionals of random fields and statistical applications (L. Sakhno).
- Application of ergodicity and stability results for Markov processes to models of risk processes and to processes in actuarial mathematics (M.Kartashov, V. Golomosiy, Y. Kartashov);
- Insurance companies with financial investment (Yu. Mishura).