Research Projects and Scientific Schools

Research project No. 22BF038-01 "Stochastic dynamical systems, heterogeneous in time or with random time: asymptotics and statistical analysis"

Academic supervisor: Mishura Yu.S.
The term of the work: 01.01.2022-31.12.2024.

The purpose of the research work: the study of general dynamical systems modeled by random processes, in particular, Levy processes, non-homogeneous Markov processes, processes with random time, processes arising as solutions of differential equations with partial derivatives and with random initial conditions, and equations with generalized fractional operators.

Performers:

• responsible executor, leading researcher Dr. Sc. L.M. Sakhno,
• senior researcher Dr. Sc. S.V. Shklyar,
• senior researcher Dr. Sc. Knopova V.P.,
• senior researcher Dr. Sc. Maiboroda R.E. (2022),
• researcher Ph.D. Golomoziy V.V. (2023),
• researcher Ph.D. I.M. Bodnarchuk (2022),
• leading engineer Ph.D. Kushnirenko S.V. (2023),
• leading engineer O.V. Lukovych (2023),
• leading engineer, Ph.D. T.O. Moklyachuk (2022).

Previous research projects

Research project No. 19BF038-01 "Exact formulas, approximations, asymptotic properties and statistical analysis of complex evolutionary systems with many degrees of freedom" (2019-2021).
Academic supervisor: Mishura Yu.S.

Research project No. 16BF038-02 "Research and statistical analysis of the asymptotic behavior of complex stochastic heterogeneous dynamic systems" (2016-2018).
Academic supervisor: Mishura Yu.S.

Research project 11BF038-02 "Evolutionary systems: research of analytical transformations, random fluctuations and statistical regularities" (2011-2015).
Academic supervisor: Mishura Yu.S.

Research project No. 06BF038-03 "Analytical and stochastic methods of dynamic systems research" (2006-2010).
Academic supervisor: Mishura Yu.S.

Research project No. 01BF038-06 "Development of the theory of random fields and dynamical systems on algebraic structures" (2001-2005).

Other projects and grants

• 1997–1998 Higher education support program, Grant KV-97 HES N4122-1, "Analytical and statistical methods in political science, sociology and psychology" (Scientific supervisor – Prof. Yadrenko M.Y.)
• "Theoretical-probabilistic and statistical analysis of stochastic dynamic systems" (grant of the Ministry of Science of Ukraine F4/309-97) (Scientific supervisor - Prof. Yadrenko M.Y.)
• 1996-1997 Tempus Tacis pre-JEP N03213-96 "Statistical Aspects of Economics: Financial mathematics, Insurance and Sample Survey in Industry and Agriculture"
• 1998-2001 TEMPUS-TACIS-JEP 10353-97 "Statistical Aspects of Economics"
• 2002-2004 TEMPUS-TACIS Network Project NP-22012-2001 "Improvement of education in economical-statistical area in Ukraine"
• 2005-2008 TEMPUS-TACIS IB-JEP-25054-2004 "Training Center for Actuaries and Financial Analysts"
• 2001-2003 NATO Collaborative linkage grant PST.CLG.976361 “Random Fields with Long-Range Dependence and Related Topics” (project coordinators Prof. M.M. Leonenko and Prof. E. Orsingher)
• 2003-2005 NATO Collaborative linkage grant PST.CLG.980408 "Fractional Calculus and Related Stochastic Processes and Equations" (coordinators Prof. Yu.V. Kozachenko and Prof. E. Orsingher).

In 2009-2011, the department participated in the Visby Program of the Swedish Institute "Extension of the Baltic-Nordic network on survey statistics to include Ukraine and possibly Belarus", the scientific leader of the project was prof. H. Kuldorff, coordinator from KNU - associate professor O.I. Vasylyk.

2009-2012 International scientific project "Multi-parameter Multi-fractional Brownian Motion" (grant of the Commission of the European Communities PIRSES-GA-2008- 230804 within the framework of the program "Marie Curie Actions"). The project was carried out jointly with the universities of Nancy (France), Cardiff (Great Britain), and Ramat Gan (Israel).

In 2009-2010, professors Yu.V. Kozachenko and Yu.S. Mishura took part in the grants of "La Trobe" University (Melbourne, Australia) "Sampling, wavelets and optimal stochastic modeling" and "Stochastic Approximation in Finance and Signal Processing" (scientific coordinator of projects - associate professor A.Ya. Olenko).

2010-2012 Grant of the State Foundation for Fundamental Research No. Ф25.1/080 "Modeling of dynamic systems by stochastic and statistical methods" (Scientific supervisor - Prof. Yu.S. Mishura)

2020-2021 Grant of the National Research Foundation of Ukraine 2020.02/0026 "Estimation of parameters, hypothesis testing and forecasting in current stochastic models" (Scientific supervisor - Prof. Yu.S. Mishura)

2023 The project "Innovative technologies for processing court decisions using machine learning algorithms", financing at the expense of the external assistance tool of the European Union to fulfill the obligations of Ukraine in the Framework program of the European Union for scientific research and innovation "Horizon 2020"" (Scientific leader - prof. Bedyukh O.R.)

Participation of department employees in scientific projects and Personal grants

Prof. Yu.S. Mishura::

• Grant of Aalto University, Finland, 2011, for visiting professorship.
• Grant of Umea University, Sweden, 2012-2015, for visiting professorship.
• Grant of Nancy University, France, 2012-2015, for visiting professorship and research work.
• Grant of University of Edmonton, Canada, 2009-2017, for visiting professorship and research work.
• Grant of the University of Lausanne, Switzerland, 2013-2018, for research work.
• ARC grant of Australia, 2015-2017, for research work.
• Grant of London Mathematical Society, 2017, for research work.
• Project STORM: Stochastics for Time-Space Risk Models, with University of Oslo, for research work, 2018-2023.
• Project "Fractional stochastic processes", October 2019, Vilnius University.
• Projects CREST JPMJCR14D7 and JPMJCR2115 of Japan Science and Technology Agency, 2018-2023
• Project granted by the Swedish Foundation for Strategic Research (SSF), within the call of SSF grants for Ukrainian scientists. The project is entitled “Fractionality: entropy and related physical properties”, 2022-2024

L.M. Sakhno::

• ARC Large Grant A10024117 “Stochastic analysis of long-range dependent multifractals” (2000-2001);
• ARC Discovery Grant DP0345577 “Statistical estimation and approximation of anomalous diffusions”(2003-2004)

G.M. Shevchenko::

• 2004, 2005 INTAS grant for young scientists
• 2010, 2013 Grant of the President of Ukraine for young scientists

K.V. Ralchenko::

• 2022-2023 International project "Diffusion and fractional diffusion processes: entropy, statistics and related physical properties" with the support of the Sydney Institute of Mathematical Sciences

Scientific schools

• "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)

More detailed information about schools - at the link:
КНУ імені Тараса Шевченка | Наукові школи - 2020

Performers of the project "Evolutionary systems: research of analytical transformations, random fluctuations and statistical regularities", 2015:
Yu. Kartashov, V. Doroshenko, K. Ralchenko, R. Maiboroda, Yu. Mishura, G. Shevchenko, S. Shklyar, T. Yanevych, L. Sakhno, Yu. Kozachenko

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 $\varphi$-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:

• Modeling of Levy processes and Levy-type processes (V.P. Knopova);
• Computer modeling of random processes and fields (T.O. Yanevych);
• Systems allowing random oscillation (O.D. Borysenko).

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).