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 |
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