Spectral theory of random fields

We study the basic spectral representations of different classes of random fields, which play the main role in probabilistic and statistical analysis of random fields. One of the first book devoted to spectral analysis of random fields is (Ivanov, Leonenko, 1989), see also (Leonenko, 1999). At the moment we work on the topic related to CMB, where spherical tensor random fields plays an key role.

Cardiff Investigators

• Prof. Nikolai Leonenko

Collaborators

Prof. Alexander Ivanov, Prof. Vo Anh, Prof. Chenshung Ma, Dr. Ludmila Sakhno, Dr. Andryi Olenko, Dr. J. Du, Dr. H.Shu

Selected publications

• Leonenko N.N., Olenko, A. (2011) Toward a computational approach to Tauberian and Abelian theorems, Methodology and Computing in Applied Probability, submitted
• Leonenko, N.N., Sakhno, L.M. (2012) On spectral representations of tensor random fields on the sphere, Stochastic Analysis and Applications, 30,1-23
• Du, J., Leonenko, N., Ma. C., Shu, H. (2012) Hyperbolic vector random fields with hyperbolic direct and cross covariance functions, Stochastic Analysis and Applications, in press
• Anh, V.V., Leonenko, N.N., Sakhno, L.M. (2006) Spectral properties of Burgers and KPZ turbulence. J. Statist. Physics, 122, N 5, 949-974
• Leonenko, N.N. (1999) Limit Theorems for Random Fields with Singular Spectrum, Mathematics and its Applications, 465. Kluwer Academic Publishers, Dordrecht/Boston/London.
• Ivanov, A.V., Leonenko, N.N. (1989) Statistical Analysis of Random Fields, Mathematics and its Applications, 28. Kluwer Academic Publishers, Dordrecht/Boston/London