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NL has 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. NL's recent focus has been on the development of the Fourth Moment Theorems for Markov chaos, the limit theorems and intermittency for a classes of ambit processes such as supOU and trawl processes, the non-local or 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.

Stories:2000-2019

Stories:1980-2000

Awards & Fellowships

Awards

  • Soros Professor (1997)

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

Education

Education

Ph.D. Central limit theorem for random fields and some problems of statistics (1976)

Science Doctor Degree (Habilitation) Limit theorems for functionals of homogeneous isotropic random fields and related topics (1990). Member of the National Academy of Sciences of Ukraine A.V. Skorokhod  was one of three referees on this Habilitation.

Collaborators

O.E. Barndorff-Nielsen, C.Heyde, M.Taqqu,  M.Meershaert, E.Merzbach, N.-R. Shieh, V.Anh, F.Avram, E. Orsingher, E.Scalas, A.V. Ivanov among the others.

Art

Zarezkii
Publication

Selected publications

Books

1. Leonenko, N.N. (1999), Limit Theorems for Random Fields with Singular Spectrum, Mathematics and its Applications, 465. Kluwer Academic Publishers, Dordrecht/Boston/London.

3. Ivanov, A.V. and Leonenko, N.N. (1989), Statistical Analysis of Random Fields, Mathematics and its Applications, 28. Kluwer Academic Publishers, Dordrecht/Boston/London. Preface of Academician A.V.Skorokhod.

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Papers

  1. Kozachenko, L.F. and Leonenko, N.N. (1987) A statistical estimate for the entropy of a random vector, Problems Infor. Transmiss., 23(2), 9-16

  2. Leonenko, N.N. and Woyczynski, W.A. (1998), Exact parabolic asymptotics for singular n-D Burgers' random fields: Gaussian approximation,  Stochastic Processes and their Applications, 76, 141-165

  3. Anh, V.V. and Leonenko, N.N. (1999) Non-Gaussian scenarios for the heat equation with singular initial conditions, Stochastic Processes and their Applications, 84, 91-114

  4. Anh, V.V. and Leonenko, N.N. (2002) Renormalization and homogenization of fractional diffusion equations with random data, Probability Theory and Related Fields, 124, N3, 381-408

  5. Anh, V.V., Heyde, C.C and Leonenko, N.N. (2002) Dynamic models of long-memory processes driven by Lévy noise with applications to finance and macroeconomics, Journal of Applied Probability, 39, N4, 730-74

  6. Barndorff-Nielsen, O.E., Leonenko, N.N. (2005) Burgers turbulence problem with linear or quadratic potential, Journal of Applied Probability, 42, N2, 550-565

  7. Heyde, C.C. and Leonenko, N.N. (2005) Student Processes, Advances of Applied Probability, 37, N2, 342-365

  8. Leonenko, N.N., Pronzato, L. and Savani, V., (2008) , A class of Renyi information estimators for multidimensional densities, 36, N5, Annals of Statistics, 2153-2182, Corrections, Annals of Statistics , 2010, 38, N6, 3837-3838

  9. Ivanov A.V., Leonenko, N.N., Ruiz-Medina, M.D. and Savich, I.N. (2013) Limit theorems for weighted non-linear transformations of Gaussian processes with singular spectra, Annals of Probability, vol. 41, No 2, 1088-1114

  10. Bourguin, S.,Campese, S.,Leonenko, N.,Taqqu, M.S.(2019); Four moments theorems on Markov chaos., Annals of Probability, 47 , no. 3, 1417–1446

  11. Grahovac, D. and  Leonenko, N. and Taqqu, M.S.(2019) Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes, Stochastic Processes and their Applications, accepted for publication 31 January 2019

  12.  Grahovac, D. ,Leonenko, N., Sikorskii, A. and Taqqu.M.S. (2019) The unusual properties of aggregated superpositions of Ornstein-Uhlenback type processes, Bernoulli, 25, N3, 2029-2050

  13. Leonenko, N.N., Taqqu, M.S. and Terdik, Gy (2018) Estimation of the covariance function of Gaussian isotropic random fields, related Rosenblatt-type distributions and the cosmic variance problem, Electronic Journal of Statistics, Vol. 12 (2018) 3114–3146

  14. Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2018) Correlated continuous time random walks and fractional Pearson diffusions, Bernoulli, Vol. 24, No. 4B, 3603-3627.

  15. Aletti, G., Leonenko, N.N. and Marzbach, E. (2018) Fractional Poisson fields and martingales, Journal of Statistical Physics, 170, N4, 700-730

  16. Grahovac, D. and  Leonenko, N and Taqqu, M.S.(2018) Intermittency of trawl processes, Statistic and Probability Letters, 137, 235-242

  17. Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2017) Heavy-tailed fractional Pearson diffusions, Stochastic Processes and their Applications, 127, N11, 3512-3535

  18. Leonenko, N., Scalas, E. and Trinh, M. (2017) The fractional non-homogeneous Poisson process, Statistic and Probability Letters, 120, 147-156

  19. Leonenko, N., Ruiz-Medina, M.D. and M.S.Taqqu (2017) Non-central limit theorems for random fields subordinated to gamma-correlated random fields, Bernoulli, 2017, Vol. 23, No. 4B, 3469-3507

  20. Anh, V.V., Leonenko, N.N. and Sikorskii, A. (2017) Stochastic representation of fractional Bessel-Riesz motion, Chaos, Solitons, Fractals, 102, 135-139

  21. Leonenko, N. and Malyarenko, A. (2017) Matern class tensor-valued ramdom fields and beyond, Journal of Statistical Physics, 168, N6, 1276-1301

  22. Denisov, D and Leonenko, N.N. (2016) Limit theorems for multifractal products of geometric stationary processes, Bernoulli, 22, N4, 2579-2608

  23. D’Ovidio, N.Leonenko and E.Orsingher (2016) Fractional spherical random fields, Statistic and Probability Letters, 116, 146-156  

  24. Avram, F., Leonenko, N.N and Sakhno, L. (2015) Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities, Stochastic Processes and their Applications, Vol 125, N4, 1629-1652 (A)

  25. Leonenko N. and Olenko, A. (2014) Sojourn measures for Student and Fisher-Snedecor random fields, Bernoulli, 20 (3), 1454-1483

  26. Leonenko, N. N.; Shieh, N-R. (2013) Rényi function for multifractal random fields. Fractals 21 , no. 2, 1350009, 13 pp.

  27. Leonenko, N.N., Meerschaert, M.M and Sikorskii, A. (2013) Fractional Pearson diffusion,  Journal of Mathematical Analysis and Applications, vol. 403, 532-546

  28. Anh, V.V, Leonenko, N.N, and Shieh N.-R., (2008), Multifractality of products geometric Ornstein-Uhlenbeck type processes, Advanced of Applied Probability, 40, N4, 1129-1156

  29. Dette, H., Leonenko, N.N., Pepelishev, A. and Zhigljavsky, A. (2009) Asymptotic optimal designs under long-range dependence error structure, Bernoulli, 15, N4, 1036-1056, Corrections Bernoulli 18 (2012), no. 2, 746  

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