Thesis supervisor: György Terdik
Location of studies (in Hungarian): University of Debrecen Faculty of Informatics Abbreviation of location of studies: DE IK
Description of the research topic:
Syllabus
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. The short range radio communication technologies and the huge amount of data transmitted slowly through sensor networks creates hot research topic from statistical analysis approach, as well.
The application of two new analytical methods can give further new interesting results for sensor network traffic. One may apply the theory of smoothly truncated Levy flights and the linear fractal model in examining the variability of traffic from self-similar to Poisson.
Bibliography
• Leonenko, N. N; Taqqu, M. S; Terdik, Gy. H. Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem. Electron. J. Statist. 12 (2018), no. 2, 3114--3146. doi:10.1214/18-EJS1473.
• Subba Rao, T, and Terdik, Gy. A New Covariance Function and Spatio‐Temporal Prediction for A Stationary Spatio‐Temporal Random Process. Journal of Time Series Analysis, Volume 38, Issue 6, 2017, 936–959
• Gy. Terdik, T. Gyires, Lévy Flights and Fractal Modeling of Internet Traffic, IEEE/ACM Transactions on Networking, VOL. 17, NO. 1, 120—129, February 2009.
• Gy. Terdik, Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis, Lecture Notes in Statistics, Springer Verlag, No142 (1999), NY.
Deadline for application: 2022-11-15
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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