• Corpus ID: 88520401

A parametric variogram model bridging between stationary and intrinsically stationary processes

@article{Schlather2014APV,
  title={A parametric variogram model bridging between stationary and intrinsically stationary processes},
  author={Martin Schlather},
  journal={arXiv: Methodology},
  year={2014}
}
  • M. Schlather
  • Published 5 December 2014
  • Mathematics
  • arXiv: Methodology
A simple variogram model with two parameters is presented that includes the power variogram for the fractional Brownian motion, a modified De Wijsian model, the generalized Cauchy model and the multiquadrics model. One parameter controls the smoothness of the process. The other parameter allows for a smooth parametrization between stationary and intrinsically stationary second order processes in a Gaussian framework, or between mixing and non-ergodic max-stable processes when modeling spatial… 
Bivariate Gaussian random fields : models, simulation, and inference
Spatial data with several components, such as observations of air temperature and pressure in a certain geographical region or the content of two metals in a geological deposit, require models

References

SHOWING 1-10 OF 25 REFERENCES
Some covariance models based on normal scale mixtures
TLDR
A new class is described that merges and generalizes various models presented in the literature, in particular models in Gneiting and Stein and nonstationary spatial covariance functions, and a multivariate extension is introduced.
Extreme values of independent stochastic processes
The maxima of independent Weiner processes spatially normalized with time scales compressed is considered and it is shown that a weak limit process exists. This limit process is stationary, and its
Efficient inference for spatial extreme value processes associated to log-Gaussian random functions
TLDR
This work considers random fields that are in the domain of attraction of a widely used class of max-stable processes, namely those constructed via manipulation of log-Gaussian random functions, and performs full likelihood inference by exploiting the methods of Stephenson & Tawn (2005), assessing the improvements in inference from both methods over pairwise likelihood methodology.
Power-law correlations, related models for long-range dependence and their simulation
  • T. Gneiting
  • Mathematics
    Journal of Applied Probability
  • 2000
Martin and Walker ((1997) J. Appl. Prob. 34, 657–670) proposed the power-law ρ(v) = c|v|-β, |v| ≥ 1, as a correlation model for stationary time series with long-memory dependence. A straightforward
Local approximation of variograms by covariance functions
Construction of Covariance Functions and Unconditional Simulation of Random Fields
TLDR
An overview over the approaches how models can be obtained in the classical approaches to geostatistics, for instance the turning bands and the random coins.
On the structure and representations of max-stable processes
We develop classification results for max-stable processes, based on their spectral representations. The structure of max-linear isometries and minimal spectral representations play important roles.
Stationary max-stable fields associated to negative definite functions.
Let Wi, i∈ℕ, be independent copies of a zero-mean Gaussian process {W(t), t∈ℝd} with stationary increments and variance σ2(t). Independently of Wi, let ∑i=1∞δUi be a Poisson point process on the real
Nonseparable, Stationary Covariance Functions for Space–Time Data
Geostatistical approaches to spatiotemporal prediction in environmental science, climatology, meteorology, and related fields rely on appropriate covariance models. This article proposes general
Multivariate Geostatistics: An Introduction with Applications
TLDR
This book presents an advanced presentation of linear models for multivariate spatial or temporal data, including the recent bilinear model of coregionalization, and an introduction to non-stationary geostatistics with a special focus on the external drift method.
...
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