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Mykola Leonenko

Professor Mykola Leonenko

Professor

School of Mathematics

Overview

I have been a Professor at Cardiff University since 2006. I joined the University as a lecturer in 2000 becoming a Reader in 2003.

I have developed an extensive and productive program of research in stochastic processes and random fields with over 260 publications, two monographs, and a textbook that have over 5,000 citations on Google Scholar. His most cited (over 680 times) paper on Leonenko-Kozachenko statistical estimate of Shannon entropy of a random vector has had a broad impact in the variety of fields, and the estimate is currently used in medical and physical equipment. My recent focus has been on the development of the Fourth Moment Theorems, the limit theorems and intermittency for supOU and trawl processes, the anomalous and/or fractional diffusion, the continuous time random walk (CTRW) models for fractional diffusion, modelling of monofractal and multifractal stochastic systems, spectral analysis of random processes and fields, homogenization and renormalization of partial differential equations with random data, limit theorems for long range dependent stochastic processes and fields and statistical analysis for random fields and their applications to data arising in neuroscience, econometrics, astrophysics and finance.

I collaborate with Profs M. Taqqu, J.Vaz, M.D. Ruiz-Medina, E.Pirozzi, A.Sikorskii, V. Anh, E. Merzbach, S. Bourguin, A.V. Ivanov and others.

Publication

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2002

2001

Articles

Research

My research interests include:

  • statistical analysis of stochastic processes and random fields
  • stochastic models for fractional diffusions
  • fractional point processes and random fields
  • ambit stochastics and intermittency
  • statistical inference for stochastic processes and random fields
  • limit theorems for functionals of random fields under weak and strong dependence
  • limit distributions of the rescaled solutions of linear and non-linear partial differential equations with random initial conditions
  • spherical random fields and CMB data
  • fractional differential equations and PDE with random data
  • statistical inference with higher-order information
  • finance and stochastics, fractal activity time risky asset modelling
  • fractional risk processes
  • multifractality for stochastic processes and random fields. Limit theorems for multifractal products of stochastic processes
  • statistical estimation of Shannon and Renyi information and statistical differences.

Research group

I am a member of the Statistics research group.

External funding since 2003

1. I was awarded an Australian Research Council Discovery grant (DP034455477) "Statistical estimation and approximation of anomalous diffusion" as Partner Investigator in collaboration with C.C. Heyde (The Australian National University) and V.V. Anh (Queensland University of Technology, Brisbane, Australia). This grant will cover years 2003-2005 with A$ 65 000 per year.

2. I was awarded an EPSRC grant EP/D057361; “Fractional Models of Anomalous Diffusion with Applications to Macroeconomics, Finance and Turbulence” GR/S10186 (RCMTO91) as Principal Investigator. This grant covered years 2003-2005 with total cost on grant £9900. This grant for collaboration with O. E. Barndorff-Nielsen (Aarhus University, Denmark), E.Orsinger (University of Roma, Italy) V.Anh Queensland University of Technology, Brisbane, Australia) and W. Woyczynski (Case Western Reserve University, Ohio,USA)

3. I was awarded an Australian Research Council Discovery grant:” Statistical modelling of spatiotemporal nonlinear diffusions processes with multifractal chracteristics” (the Project ID: DP0559807) as Partner Investigator in collaboration with V.V. Anh (Queensland University of Technology, Brisbane, Australia), Lau, K.S. (Chinese University of Hong Kong), Angulo, J. M. and Ruiz-Medina, L.M. (University of Granada, Spain) .This grant covers years 2005-2009 with A$ 353 000.
4. I was awarded a new EPSRC grant EP/D057361 (RCMT119): “Limit theorems for spatio-temporal random fields and related topics” as Principal Investigator for the years 2006-2009 with total cost £10379. This grant is for collaboration with C.C. Heyde (The Australian National University and Columbia University, USA), M.S. Taqqu (Boston University, USA), V.Anh (Queensland University of Technology, Brisbane, Australia) and E. Taufer (University of Trento, Italy).

5. I was awarded a grant supported of DGI (Dirección General de Investigación) of Ministry of Education and Science of Spain, and FEDER funds (European funds) for collaboration with professors J.M. Angulo and Maria D. Ruiz Medina (University of Granada, Spain). The title of the grant is: Modelling and Statistical Analysis of Local Characteristics and Memory Properties for Spatiotemporal Data. REFERENCE NUMBER: MTM2005-08597. This grant covers years 2005-2008 with 48000 €.

6. I am a partner investigator on the JSPS (Japan) grant project “Advances and new methods for prediction theory and Tauberian theorems with application to stochastic analysis of stochastic processes with memory” (the Principal Investigator is A/Prof. A. Inoue, Department of Mathematics, Hokkaido University, Japan).

7. Grant of London Mathematical Society (2007) 2632 for invitation to UK (Edinburg, Cardiff, Swansea) professor Florin Avram (University of Pau, France), £1000.

8. I was awarded a grant supported of DGI (Dirección General de Investigación) of Ministry of Education and Science of Spain, and FEDER funds (European funds) for collaboration with professors M. D. Ruiz Medina and J.M. Angulo (University of Granada, Spain). The title of the grant is: Wavelet Methods for Inference from Functional Data in Singular Spaces. REFERENCE NUMBER: MTM2008-03903. This grant covers years 2009-2011 with 27000 € .

9. I am Principal Investigator of the Grant RCMT152 Commission of the European Communities PIRSES-GA-2008-230804 (Marie Curie) “Multi-parameter Multi-fractional Brownian Motion” for collaboration of Cardiff University and CNRS, Nancy (France); Kyiv National Taras Shevchenko University (Ukraine) and Bar Ilan University (Israel). This grant covers years 2009-2012 with 90000 € .

10. I am a Partner Investigator of a grant of Ministry of Education and Science of Spain, MTM2012-32674, Project Title: Limit theorems for spatiotemporal processes and asymptotic functional inference with applications to the analysis of climate change, CDNA microarray and finance structure of firms.
Team: N:N. Leonenko, R.M. Espejo, R Fernández-Pascual, M.P. Frías, R.
Román and M.D. Ruiz-Medina. This grant covers years 2012-2015 with 26900 € .


11. I am a Partner Investigator of the  Australian Research Grant (ARC) Discovery Project DP 160101366. This grant covers years 2016-2019 with A$ 324 686. Project title: New Method in Theory and Applications of Spherical Random Fields, Team: Prof. Ph. Broadbridge and Dr A.Olenko ((La Trobe University, Melbourne, Australia), Prof. V.Anh (Queensland University of Technology, Brisbane, Australia), Prof. N.Leonenko (Cardiff University,UK).

12. I am Partner Investigator of the of a grant of Ministry of Education and Science of Spain, MTM2015-71839-P, Project Title: Random Fields Functionals, Asymptotic Theory and Inference”
Team: N:N. Leonenko, R.M. Espejo, R Fernández-Pascual,  M.P. Frías, J.A.Liebena and M.D. Ruiz-Medina. This grant covers years 2016-2019 with 25100 € .

13. I am a Principal Investigator of the  Cardiff Incoming Collaboration Seedcorn Fund (collaboration with M.S.Taqqu), £8780, 2015-2017.

14. I am a Principal Investigator of the  Cardiff  Data Innovation Research Institute Seed Corn Funding ( with P.Coles, Cardiff University), £ 5450, 2017.

15. I am a Partner Investigator of the scientific project funded by J.J. Strossmayer University of Osijek, Croatia. It covers  years 2017-2018 with £5277 (or 45000 HRK). The title of the project is “Stochastic models with long-range dependence”. Team: N.N. Leonenko, D. Grahovac, I. Papić, N. Šuvak.

16. I am a Partner Investigator of the scientific project funded by J.J. Strossmayer University of Osijek, Croatia. It covers  years 2018-2020 with £3727 (or 31.882,50 HRK). The title of the project is “Limiting behaviour of intermitten processes and diffusions”. Team: D. Grahovac (Project leader),N.Leonenko, M.Taqqu.

17.ARC grant (Discovery) ID DP220101680  “Random fields: non-Gaussian stochastic models and approximation schemes”.  Participant Type: Partner Investigator (Principal Investigators Prof. Philip Broadbridge, A/Prof. A.Olenko La Trobe University, Melbourne, Australia; Prof. A.Ayache, University of Lille, France), 2022-2025, AU$ 422680.

18. Received a grant of USD 10,000 from MHRD (India) in collaboration with Dr. Arun Kumar (IIT Ropar) to conduct a research level GIAN course of duration 5 days, entitled with "Risky Asset Models with Dependence (191010K02 ) at Indian Institute of Technology (IIT) Ropar during September 2021

19. Grant of London Mathematical Society, Ref. 42007 (£1200).

20.   I am a Partner Investigator of the scientific project founded by FAPESP 22/09201-8 (Brazil), for collaboration with Prof. J.Vaz (Principal Investigated), 2022-2023, 31000R(5270£).

21. I participated in the programme Fractional Differential Equations (FDE2) (January-April 2022) in Isaac Newton Institute forMathematical Sciences, Cambridge, UK.

22.  I am also  participating in the programme Uncertainly Quantification and Modelling of Material Programme (August 2023) in Isaac Newton Institute for Mathematical Sciences, Cambridge.

23.   I am Partner Investigator of  the Croatian Scientific Foundation (HRZZ) grant Scaling in Stochastic Models (IP-2022-10-8081), 2023-2027, Euro 176742.32, Principar Investigator Dr.D.Grahovac.

Teaching

Undergraduate

  • MA3503 Stochastic Processes for Finance and Insurance

Postgraduate

  • MAT011 Financial Maths & Modern Acturial Risk Theory

Biography

I graduated with an MSc from Mathematical-Mechanics Faculty of Kyiv University in 1973.

My PhD in Physics and Mathematics (Probability Theory and Mathematical Statistics) was from Moscow Institute for Electronic Constructions (MIEM) in 1976. PhD title, Central limit theorem for random fields and some problems of statistics.

In 1990 I was awarded my Doctor of Science Degree (Habilitation) in Physics and Mathematics (Probability Theory and Mathematical Statistics) from Institute of Mathematics Academy of Sciences of Ukraine, Kyiv. Title: Limit theorems for functionals of homogeneous isotropic random fields and related topics.

Honours and awards

N. M. Krylov medal of Academy of Science of Ukraine (1993), the highest annual award for mathematicians in Ukraine.

Professional memberships

Membership in the American Mathematical Society, London Mathematical Society and Kyiv Mathematical Society.

Academic positions

  • 1973-1976 Engineer, Inst. of Cybernetics Acad. of Sci. of Ukraine, Kyiv
  • 1976-1977 Senior Scientific Researcher, Inst. of Cybernetics Acad. of Sci. of Ukraine, Kyiv
  • 1977-1980 Assistant-professor, Kyiv University
  • 1980-1991 Associate professor, Kyiv University
  • 1991-2002 Professor, Kyiv University
  • 1999-2000 Research/Senior Research Associate in Statistics, Queensland University of  Technology, Brisbane

Committees and reviewing

Deputy Editor-in-Chief  of the following journal: 

      Theory of Probability and Mathematical Statistics, Publisher AMS (USA), ISSN 1547-7363

Member of editorial board of the following journals:

  • Fractional Calculsus and Applied Analysis, Springer, ISSN 13110454, 13142224
  • Random Operators and Stochastic Equations (publ. Walter de Gruyter , Berlin, New York), ISSN 0926-636
  • Mathematical Communications (publ. Ele-Maths journals), ISSN 1331-0623
  • Bulletin of National Taras Shevchenko University of Kyiv (Publisher: Kyiv University, Ukraine), ISSN 1684-1565.
  • I was a Guest Editor of the Special Issue of  International Journal of Differential Equations "Fractional Differential Equations" (jointly with F.Liu, M.Meerschaert, Sh. Momani, W.Chen and Om Agrawal), 2010, ISSN  1687-9643
  • I was a Guest Editor of the Special Issue of  International Journal of Differential Equations "Fractional Differential Equations" (jointly with F.Liu, Om Agrawal, Sh. Momani and  W.Chen), 2011, ISSN  1687-9643Major honours and distinctions

Supervisions

Current supervision

Ahlam Alghamdi

Ahlam Alghamdi

Research student

Zoe Salinger

Zoe Salinger

Research student

Contact Details

Email LeonenkoN@cardiff.ac.uk
Telephone +44 29208 75521
Campuses Abacws, Room 3.59, Senghennydd Road, Cathays, Cardiff, CF24 4AG

Research themes

Specialisms

  • Probability theory

External profiles