Stochastic modelling and statistical analysis of spatial and long-range dependent data. (English) Zbl 1502.60079
From the text: This thesis mainly studies long-range dependent
stochastic processes. The main objective of this thesis is to study and develop stochastic
models and statistical methods for spatial and temporal long-range dependent data.
MSC:
| 60G60 | Random fields |
| 62M15 | Inference from stochastic processes and spectral analysis |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62P12 | Applications of statistics to environmental and related topics |
Keywords:
spherical random fields; multifractality; multifractionality; Rényi function; cosmic microwave background radiation; asymptotic normality; cyclic long-memoryReferences:
| [1] | Alomari, H., Ayache, A., Fradon, M. and Olenko, A., ‘Estimation of cyclic long-memory parameters’, Scand. J. Stat.47(1) (2020), 104-133. · Zbl 1444.62097 |
| [2] | Ayache, A., Fradon, M., Nanayakkara, R. and Olenko, A., ‘Asymptotic normality of simultaneous estimators of cyclic long-memory processes’, Electron. J. Stat.16(1) (2022), 84-115. · Zbl 1498.62175 |
| [3] | Ayache, A. and Véhel, J., ‘On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion’, Stochastic Process. Appl.111(1) (2004), 119-156. · Zbl 1079.60029 |
| [4] | Broadbridge, P., Nanayakkara, R. and Olenko, A., ‘On multifractionality of spherical random fields with cosmological applications’, ANZIAM J., to appear. · Zbl 1505.60055 |
| [5] | Leonenko, N., Nanayakkara, R. and Olenko, A., ‘Analysis of spherical monofractal and multifractal random fields’, Stoch. Environ. Res. Risk. Assess.35(3) (2021), 681-701. |
| [6] | Leonenko, N. and Shieh, N.-R., ‘Rényi function for multifractal random fields’, Fractals21(2) (2013), Article no. 1350009. · Zbl 1278.28003 |
| [7] | Marinucci, D. and Peccati, G., Random Fields on the Sphere: Representation, Limit Theorems and Cosmological Applications (Cambridge University Press, New York, 2011). · Zbl 1260.60004 |
| [8] | Olenko, A.. ‘Limit theorems for weighted functionals of cyclical long-range dependent random fields’, Stoch. Anal. Appl.31(2) (2013), 199-213. · Zbl 1267.60056 |
| [9] | Yadrenko, M., Spectral Theory of Random Fields (Optimization Software, New York, 1983). · Zbl 0539.60048 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
