CA24104 Stochastic Differential Equations: Computation, Inference, Applications (OC-2024-1-27157)

SUMMARY

Stochastic differential equations (SDEs) are used to model phenomena under the influence of random noise and uncertainty and are useful in an extraordinary range of applications. In health, SDE models of tumour growth can help medical practitioners design interventions. In clean energy, they can model airflow around wind turbine blades, and enable multiscale modelling of entire wind farms and energy grids by representing small scale effects as noise. In computing, SDEs can be used to develop training algorithms for deep learning algorithms

The development and effective deployment of stochastic models requires input from a broad range of specialist experts: applied modellers, theoretical mathematicians, numerical analysts, and statisticians, all guided by the needs of stakeholders in academia and industry. However, in the current European research landscape, there is no large scale framework enabling these communities to interact, and opportunities for goal-driven research progress that is informed by all relevant expertise are being lost.

Under the umbrella of computational stochastics, STOCHASTICA will bring together members of all of these communities to create a network of researchers with common goals informed by academic and industry partners. The work of the Action will generate a computational toolbox including a database of test problems, implementation guidance, and accessible descriptions of mathematical quality that empower non-specialist experts to make appropriate and routine use of stochastic models in applications such as natural resource management, renewable energy transmission, medical and public health applications including epidemiology and models of tumour growth.

SCIENTIFIC SCOPE	Areas of Expertise	Keywords
1. Mathematics:	Numerical analysis	1. Stochastic modelling
2. Mathematics:	Probability	2. Qualitative analysis
3. Mathematics:	ODE and dynamical systems	3. Numerical approximation methods
4. Mathematics:	Statistics	4. Bayesian inference
5. Mathematics:	Theoretical aspects of partial differential equations

COST Members

Main Proposer: Ireland Network of Proposers:
Full Member: Austria, France, Germany, Greece, Hungary, Ireland, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Spain, Sweden, Turkiye, Ukraine, United Kingdom
Main and secondary proposers: 25,00% YRI / 50,00% Women / 50,00% ITC

Specific Organisations

European RTD Organisation: Foundation for Research and Technology – Hellas
Industrial Dimension
SMEs: Poland, Ukraine
Large companies: France, Netherlands

The group of investigators from the department of Probability, Statistics and Actuarial mathematics will participate with Prof. Yuliya Mishura as the team leader.

Legal Case Law Analytics: Exploring Big Data Insights through AI-Driven Statistical Modeling” ( 2025-2026)

Ukrainian-Swedish project (jointly with Linneus University)

The project is aimed at researching innovative tools for analyzing large data sets of court decisions in the Unified State Register in order to summarize them, as well as applying modern statistical and artificial intelligence methods. This will provide an objective understanding of the efficiency of the judicial system and allow for better allocation of resources and strengthening of public trust.

Visit the project website for more details.

Previous research projects

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).

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