The following are the most important research results:
1. momentum equations were built for a sequence of random transformations depending on finite-valued semi-Markovian processes; the stability of solutions was studied in various probabilistic interpretations;
2. momentum equations were obtained for solutions of systems of linear differential and incremental equations, whose coefficients depend on semi-Markovian processes in case of the discontinuities in their solutions occurring simultaneously with discontinuities of the random process;
3. equations were obtained for the first and second moments for solutions of systems of linear incremental equations with random coefficients depending on a finite-valued semi-Markovian chain in case of the simultaneity of discontinuities of a random chain and random transformations of their solutions; necessary and sufficient criteria of the stability of solutions on the average and the quadratic average were found;
4. the necessary and sufficient criteria of the stability, and the quadratic average stability of solutions of systems of linear differential equations with coefficients depending on a semi-Markovian process were obtained on condition of the simultaneity of discontinuities of the semi-Markovian process and random transformations of the system solutions, et al.
Theoretical, methodological and applied recommendations, which have been developed, make it possible to broaden the existing mathematical apparatus of the optimisation of dynamic systems in conditions of uncertainty and conflict. For instance, a number of tasks related to political technologies and banking (including tasks of the projection of various election-related situations) were solved in accordance with the suggested concept. Some results are used for the presentation of lectures at the Advanced Mathematics Department of the Information Systems and Technologies Faculty of Vadym Hetman Kyiv National Economics University in Multidimensional Data Analysis (certificate No. 11.04 of 5 March 2009).
Areas of Scientific Studies:
1. Research, resilience and numerical/analytical methods of building solutions of differential and integral equations using computers
2. Research into the stability of solutions of differential and incremental equations with determined or stochastic coefficients
3. Optimisation of linear dynamic systems
4. Research into the stability of solutions of linear and non-linear differential equations with determined stochastic coefficients
5. Optimisation of solutions of linear and non-linear differential and incremental equations with determined or stochastic coefficients
6. Synthesis of optimum controls for linear dynamic systems with determined or stochastic coefficients.
Last redaction: 14.12.16