Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-13T12:25:58.758Z Has data issue: false hasContentIssue false
  • English
  • Français

ON ASYMPTOTICS OF FUNCTIONALS OF RANDOM FIELDS WITH LONG-RANGE DEPENDENCE

Part of: Limit theorems Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  20 February 2020

TAREQ ALODAT Open the ORCID record for TAREQ ALODAT [Opens in a new window]
TAREQ ALODAT*
Affiliation:
Department of Mathematics and Statistics,La Trobe University, Melbourne, Victoria3086, Australia email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'

Keywords

long-range dependenceHermite distributionsadditive functionalsfiltered random fieldsself-similar processes

MSC classification

Primary: 60G60: Random fields
Secondary: 60F17: Functional limit theorems; invariance principles 62M30: Spatial processes 62M40: Random fields; image analysis
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 3 , June 2020 , pp. 518 - 521
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Footnotes

Thesis submitted to La Trobe University in September 2019; degree approved on 11 December 2019; principal supervisor Andriy Olenko, co-supervisor Agus Salim.

References

Alodat, T., Leonenko, N. and Olenko, A., ‘Limit theorems for filtered long-range dependent random fields’, Stochastics (to appear).Google Scholar
Alodat, T. and Olenko, A., ‘Weak convergence of weighted additive functionals of long-range dependent fields’, Theory Probab. Math. Statist. 97 (2017), 9–23.Google Scholar
Alodat, T. and Olenko, A., ‘Asymptotic behaviour of discretized functionals of long-range dependent functional data’, Comm. Statist. Theory Methods (to appear).Google Scholar
Beran, J., Feng, Y., Ghosh, S. and Kulik, R., Long-Memory Processes (Springer, Berlin, 2013).CrossRefGoogle Scholar
Doukhan, P., Oppenheim, G. and Taqqu, M. S., Theory and Applications of Long-Range Dependence (Birkhäuser, Boston, 2002).Google Scholar
Ivanov, A. and Leonenko, N., Statistical Analysis of Random Fields (Springer, Dordrecht, 1989).CrossRefGoogle Scholar
Leonenko, N. and Olenko, A., ‘Tauberian and Abelian theorems for long-range dependent random fields’, Methodol. Comput. Appl. Probab. 15(4) (2013), 715–742.CrossRefGoogle Scholar
Leonenko, N. and Olenko, A., ‘Sojourn measures of Student and Fisher–Snedecor random fields’, Bernoulli 20(3) (2014), 1454–1483.10.3150/13-BEJ529CrossRefGoogle Scholar
Leonenko, N. and Taufer, E., ‘Weak convergence of functionals of stationary long memory processes to Rosenblatt-type distributions’, J. Statist. Plann. Inference 136(4) (2006), 1220–1236.CrossRefGoogle Scholar
Major, P., ‘Limit theorems for non-linear functionals of Gaussian sequences’, Z. Wahrsch. verw. Gebiete 57(1) (1981), 129–158.CrossRefGoogle Scholar
Rosenblatt, M., ‘Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables’, Probab. Theory Related Fields 49(2) (1979), 125–132.Google Scholar