Thesis supervisor: György Terdik
Location of studies (in Hungarian): Debreceni Egyetem Informatikai Kar Abbreviation of location of studies: DE IK
Description of the research topic:
In recent years it has become necessary to develop statistical methods for the analysis of data coming from diverse areas such as, environment, marine biology, agriculture, finance etc. The data which comes from these areas, are usually, functions of both space and time. Any statistical method developed must take into account both spatial dependence, temporal dependence and any interaction between space and time. There is a vast literature on statistical analysis of stationary spatial data but not to the same extent in the case of stationary spatio-temporal data. The inclusion of an extra temporal dimension, which cannot be imbedded into spatial dimension gives raise to many problems. One such problem is finding a suitable covariance function which is positive definite and depends on spatial lag difference and temporal lag.
In several fields of sciences like geophysics, astrophysics, climatology etc. we come across observations which are non-Gaussian. One can characterizes a Gaussian process by its first two moments, namely, mean, variance and autocorrelations (or equivalently second order spectrum). Although second order properties of Gaussian fields are well established, characterization of non-Gaussian fields which require study of higher moments (or equivalently higher order spectra) are not well known
Bibliography
• György Terdik, Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis, Lecture Notes in Statistics, Springer Verlag, No142 (1999), New York,
• T. Subba Rao and Gy. Terdik (2012), Statistical Analysis of Spatio-temporal Models and Their Applications, Ch. 18, Handbook of Statistics, Vol. 30, ISSN: 0169-7161 18, 2012 Elsevier B.V., DOI: 10.1016/B978-0-444-53858-1.00018-1, p.521-541
• Iglói, E. and Terdik, Gy., Superposition of diffusions with linear generator and its multifractal limit process, ESAIM Probab. Stat., 7, 23—88, 2003.
Recommended language skills (in Hungarian): angol Number of students who can be accepted: 1
Deadline for application: 2018-02-16
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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