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ON STATISTICAL PROPERTIES OF NONLINEAR FUNCTIONALS OF RANDOM FIELDS

Part of: Limit theorems Stochastic processes Sequential methods Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  18 September 2020

DAREEN OMARI Open the ORCID record for DAREEN OMARI [Opens in a new window]
DAREEN OMARI*
Affiliation:
Department of Mathematics and Statistics, La Trobe University, Melbourne, Victoria, 3086, Australia
*
e-mail: [email protected]
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Abstract

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Keywords

reduction principlelong-range dependenceshort-range dependencenoncentral limit theoremsHermite distributionsstochastic partial differential equationsspherical random fields

MSC classification

Primary: 60G60: Random fields
Secondary: 35R01: Partial differential equations on manifolds 60F17: Functional limit theorems; invariance principles 62L20: Stochastic approximation
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 2 , April 2021 , pp. 338 - 340
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Footnotes

Thesis submitted to La Trobe University in December 2019; degree approved on 8 April 2020; principal supervisor Andriy Olenko, co-supervisor Luke Prendergast.

References

Anh, V., Broadbridge, P., Olenko, A. and Wang, Y., ‘On approximation for fractional stochastic partial differential equations on the sphere’, Stoch. Env. Res. Risk. 32(9) (2018), 2585–2603.CrossRefGoogle Scholar
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Broadbridge, P., Kolesnik, A. D., Leonenko, N., Olenko, A. and Omari, D., ‘Spherically restricted random hyperbolic diffusion’, Entropy 22(2) (2020), Article ID 217.CrossRefGoogle ScholarPubMed
Doukhan, P., Oppenheim, G. and Taqqu, M. S., Theory and Applications of Long-Range Dependence (Birkhäuser, Boston, MA, 2002).Google Scholar
Ivanov, A. and Leonenko, L., 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.CrossRefGoogle Scholar
Olenko, A. and Omari, D., ‘Reduction principle for functionals of vector random fields’, Methodol. Comput. Appl. Probab. 22 (2020), 573–598.CrossRefGoogle Scholar
Olenko, A. and Omari, D., ‘Reduction principle for functionals of strong-weak dependent vector random fields’, Braz. J. Probab. Stat. (2020), to appear.CrossRefGoogle Scholar