# Scientific research

### Main areas of department's scientific research are:

- stochastic systems and networks theory;
- asymptotic analysis of branching processes;
- statistics of random processes and fields;
- data analysis;
- econometrics;
- methods of statistical forecasting;
- actuarial mathematics;
- financial mathematics;
- risk theory;
- asymptotic methods in statistics of stochastic models;
- algorithms of system estimation under uncertainty;
- modeling random systems, processes and fields;
- mathematical methods of experiment planning;
- development of distant courses of probabilistic profile;
- development of statistical software and tools for data analysis;
- computer networks and Internet technologies.

Scientific research and educational activities are made in cooperation with Probabilistic-statistical Methods laboratory, that was founded in 1983 on the basis of Department of Applied statistics. Laboratory consolidates scientific researchers and lecturers for work on actual researches, development of educational process, involvement of students and postgraduates for solving of important scientific problems. Laboratory employees are involved into educational process in such courses as probability theory and mathematical statistics, data analysis, applied statistical software, econometrics, actuarial mathematics, sample studies, social statistics.

Department of applied statistics in collaboration with department of system analysis and decision making theory and operations research department handles annual International Conference Problems of Decision Making under Uncertainties (PDMU) starting from 2001.

### Main scientific developments of Department of applied statistics and Probabilistic-statistical Methods laboratory are:

- methods of diffusion and Gaussian approximation were developed for a wide class of stochastic systems with Markovian and semi-markovian interruption times and became a grounding for new approach of research of real-life informational and computational networks and modern communication systems;
- new results on asymptotic analysis of multichannel stochastic networks were obtained: asymptotic properties of steady state distribution were researched, results of law of averages and central limit theorem type were proved for steady state distribution of the network under critical load;
- limit theorems were proved for stochastic systems with slowly changing properties and phase space, that allows asymptotic state enlargement;
- online algorithms based on pseudoinverse operators of parameter estimation were developed for linear, bilinear and nonlinear systems under uncertainty conditions and non-classical assumptions; asymptotic analysis of developed algorithms was performed;
- STADEX statistical package was developed for statistical analysis of passive observations, experimental planning, time series analysis, multidimensional statistical analysis. STADEX was used in research of marine, selection of material's optimal properties in space technologies, analysis of Ukrainian small business sector, data analysis in sociology, economics, medicine, complicated production objects and technological processes;
- OMEGA platform for distant courses along with a set of courses on social statistics, probability theory and mathematical statistics was developed.

7 doctorial and more than 50 Ph.D. researches were prepared by researchers of Department of applied statistics. 10 monographs, 25 textbooks and more than 500 articles were published.

Researches and scientific results of lecturers and researchers of department were deserve rewarded by a number of awards: professor Anisimov V.V. was honored by reward of Academy of science's president for young scientists (1975), Yaroslav Mudry Academy of science of Ukraine award (1995), IRF grant (1996); Grishchenko V.O.,Voina O.A., Lebedev E.A. - CC LKSM Ukraine and Ukrainian Republican Council of NTT first prize (1983); professor Donchenko V.S. - reward of Academy of science's president for young scientists (1978); Voina O.A., Slabospitsky O.S., Cherniak O.I. - IRF grants (1995); Lebedev E.A. - IRF grant (1997); Sidorov M.V. - IRF grant and reward of Academy of science's president for young scientists (1996).

Graduates of the department of applied statistics, that became doctors of science, were working in laboratory: Lebedev E.A. (senior researcher, head of laboratory, 1983-1987), Yurachkivskyy A.P. (junior researcher, 1984-1988), Doctor of Economics Chernyak O.I. (researcher, 1983-1986); Ph.D. on Physics and Mathematics Lukashuk L.I. (head of laboratory, 1987-1993), Grishchenko V.A., Litvin I.M., Nechayev I.G., Pushkin S.G., Sereda V.I., Sityuk V.N., Smirnova V.V., Chechelnitsky O.A.

Head of Laboratory (1993-2006), Senior Researcher, Ph.D. Tovmachenko N.M., Senior Researcher, Ph.D. Mudrak N.V., junior researchers Berezhnaya N.M., Demchenko S.I., Dyachkivska N.A., PetrenkoO.R., Sichkar I.M., Sorokin S.B., senior software engineer Zabolotnaya L.V., senior engineer Krupnik V.M., senior engineers Kozachenko L.F., Kulish O.V., Lazarenko L.V., Lugnih T.A., Makarevich (Malyuga) O.S., Repin K.Y., software engineer Leonenko O.V., engineer of first category Yanok A.V., engineers Gaikovich N.A., Marchuk O.S., Matveychik O.K., Murzin V.S., Radionova T.I., Rajko O.V., Semenchenko Y.A., Yatsyuk N.V., senior technician Mazur K.I., laboratory Grigoryan I.V., Dunduchenko O.E., Kisel I.M., Kuzmenko O.B., Lanchuk O.V., Mai O.V., Plyashkova H.P., anatomist Korzhenko L.D.,Nazarenko T.V. were working in Probabilistic-statistical Methods laboratory in different years.