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Professor Nikolai Leonenko

Professor Nikolai Leonenko

Professor

School of Mathematics

Email
leonenkon@cardiff.ac.uk
Telephone
+44 (0)29 2087 5521
Campuses
M/2.38, 2nd Floor, Mathematics Institute, Senghennydd Road, Cardiff, CF24 4AG

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 250 publications, two monographs, and a textbook that have over 4,000 citations on Google Scholar. His most cited (over 500 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 and statistical analysis for random fields and their applications to data arising in neuroscience, econometrics, astrophysics and finance.

I collaborate with Profs O. Bardorff-Nielsen, C. Heyde, M. Taqqu, M.D. Ruiz-Medina, V. Anh, E. Merzbach, M. Meerschaert, S. Bourguin, A.V. Ivanov and others.

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

Speaking engagements

Major conference talks since 2004

Invited Lectures Since 2004:

  • 2nd Spanish Workshop on Spatio-Temporal Modelling of Environment Processes, (Granada, Spain, 2004), Invited Lecture
  • Workshop on Stochastic Processes and Related Topics, (Swansea, UK, 2005), Invited Lecture
  • International Conference: Modern Problems and New Trends in probability Theory (Chernivtsi, Ukraine, 2005), Invited Lecture
  • W-optimal design and related statistical issues (Jouan les Pins, France, 2005), Invited Lecture
  • Modern stochastics: theory and applications (Kyiv, Ukraine, 2006), Invited Lecture, Organiser of Section: Limit theorems.
  • Workshop on Stochastic Analysis, (Swansea, UK, 2007), Invited Lecture.
  • Workshop “Recent Developments in Finance and Applied Statistics” (National Australian University, Canberra, Australia, 2007), Invited Lecture
  • Statistics for Dependent Data (StatsDep) (Paris, France, 2008), Invited Lecture.
  • Croatian Congress of Mathematics (Osijek, Croatia, 2008), Invited Lecture.
  • International Conference “Stochastic Analysis and Random Dynamical Systems”(Lviv, June 14-20, 2009), Invited Lecture.
  • 10th International Vilnius Conference on Probability and Statistics (Vilnius, Lithuania, 2010), Invited Lecture.
  • Modern Stochastics: Theory and Applications II (2010, Kyiv, Ukraine), Invited Lecture, Organiser of Section: Limit theorems.
  • University of Swansea, Wales (June 2011) Workshop “Fractional Calculus and Random Processes”, Invited Lecture.
  • International Conference on Long-Range Dependence, Self-Similarity, and Heavy Tails. In honor of Professor Murad S.Taqqu, North Carolina, 19-21 April, 2012.
  • Non-Stationarity in Statistics and Risk Management, Paris, France, 2-5 July 2012, Invited Lecture.
  • Modern Stochastics: Theory and Applications III(2012, Kyiv, Ukraine), Invited Lecture, Organiser of Section: Limit theorems
  • Non-Stationarity in Statistics and Risk Management, CIRM, Luminy, France, 21-25 January 2013, Invited Lecture
  • Modern trends in Markov processes and queuing theory, Workshop, Cardiff University, UK, 15 February 2013, Organiser (jointly with Prof. J.Griffiths).
  • 18th European Young Statistical Meeting, Osijek (Croatia), 26-30 August, 2013, Keynote lecture.(http://www.mathos.unios.hr/eysm18/)
  • Probabilistic and Statistical Techniques for Cosmological Applications, Rome, Italy, 5-7 June, 2013, Invited Speaker
  • Workshop: Multifractal Analysis: From Theory to Applications and Back, Banff, Canada, 23-28 February 2014 (http://www.birs.ca/events/2014/5-day-workshops/14w5045), Poster.
  • Probablity, Reliability and Stochastic Optimazation, Kyv, April 7-10, 2015, Inivted Lecture.
  • Stochastic Analysis and Risk Management in Financial Markets, Workshop, Cardiff University, UK, 8 May 2015, Organiser (jointly with Prof. P.Harper).
  •  Fractality and Fractionality, Worshop, Lorenz Center, Leiden, The Netherland, 17-20 May, 2016, Invited Lecture.
  • Probability, Non-Local Operators and Applications, Brighton, University of Sussex, 2-3 June, 2016, Invited Lecture.
  • World Congress: 11th Intrenational Conference on Mathematical Problems in Engineering, Aerospace and Sciences, La Rochelle, France, 5-8 July, 2016; Invited Lecture.
  • Conference in Honor of Enzo Orsingher, Rome, 23 September, 2016; Invited Lecture.
  • 17 th Applied Stochastic Models and Data Analysis International Conference, 6-9 June 2017, London, UK,  Invited Lecture.
  • Workshop “Isotropic Random Fields in Astrophysics”, 29- 30 June 2017, Cardiff, UK, Organiser (with P. Coles), see http://ssa.cf.ac.uk/randomfields/
  • Second Conference on Ambit Fields and Related Topics, Aarhus University, Denmark, 14-16 August 2017, Invited Speaker.
  • 8th Meeting South-West Netwrok of the LMS Network in Generalised Solutions for Nonlinear PDEs,Cardiff, 25 September  2017, Invited Speaker.
  • International Conference on Stochastic Processes and Algebraic Strucures, Stockholm and   Mälardalen University, Sweden, October, 4-6, 2017, Keynote speaker.
  •  Workshop “Fractional Calculus, Probablity  and Non-local Operators: Applications and Recent Developments, Bilbao, Spain, Novemer 8-10, 2017, Invited Speaker.
  • Conference on Nonstationarity, Paris, France, June 4-6,2018, Invited Speaker
  • 9TH International Workshop on Applied Probablity (IWAP 2018), June 18-21, 2018, Budapest, Hungary, Invited Speaker.
  • International Conference «Stochastic Equations, Limit Theorems and Statistics of Stochastic Processes», dedicated to the 100th anniversary of I.I.Gikhman, September 17-22, 2018, Kyiv, Ukraine, Invited Speaker.
  •  MAM Workshop in Probablity Theory, Mathematical Statistics and Applications, November 21, Malardalen University, Vasteros, Sweden, Invited Speaker.
  • Second Italian Meeting on Probability and Mathematical Statistics, Vietri sul Mare, 17-20 June, 2019, Invited Speaker.
  • Fourth Conference on Ambit Fields and Related Topics, Sonderborg, Denmark, 5-8 August 2019, Invited Speaker,
    http://math.au.dk/events/2019/ambitfields4
  • Workshop “Estimation of entropies and other functionals:Statisitcs meets information theory”, 9-11 September 2019, Cambridge, Centre for Mathematical Sciences, University of Cambridge, UK, Organiser (with T.Berrett, R.Lockhart, R. Samworth, Y.Wu), see
    http://www.statslab.cam.ac.uk/~tbb26/WorkshopIndex.html
  •  MSTA-5:Modern Stochstics: Theory and Applications, 2-5 June 2020, Kyiv, Ukraine, Invited Speaker ,see  http://probability.univ.kiev.ua/msta5/
  • International Workshop IWSPA-2020: “Stochastic processes and Their Applications, Madrid (Spain), 25-26 June 2020, , Keynote speaker, see
    http://blogs.mat.ucm.es/presa/workshop/
  • 8 European Congress of Mathematician, Slovenia, 5-11 July 2020, Minisimposium ID18, Invited Speaker, see https://www.8ecm.si/

Committees and reviewing

Member of editorial board of the following journals:

  • Random Operators and Stochastic Equations (publ. Walter de Gruyter , Berlin, New York), ISSN 0926-6364
  • Theory of Probability and Mathematical Statistics (publ. AMS (USA)), ISSN 1547-7363
  • 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

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Undergraduate

  • MA3503 Stochastic Processes for Finance and Insurance

Postgraduate

  • MAT011 Financial Maths & Modern Acturial Risk Theory

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.

Past projects

I supervised 14 PhD students overall.

Graduate students advised at Cardiff University:

  1. E. Taufer (2002-2004): passed PhD examination in December 2004;
  2. Bakeerathan Gunaratnam (2006-2007): passed examination in December 2007 (M. Phil program).
  3. S. Petherick (2007-2010), PhD, passed in 2011.
  4. A.Kerss (2011-2014), PhD, passed in 2014.
  5. M.S.Cadirci (2018-2021), PhD.
  6. Z.Salinger (2019-2022),PhD

External profiles