A class of non-Gaussian second order random fields

Åberg, Sofia; Podgórski, Krzysztof

doi:10.1007/s10687-010-0119-1

Cited by 30 publications

(49 citation statements)

References 20 publications

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“…The model coincides with the one that in the discretized version was given by (1). Dynamics is expressed by an arbitrary time varying velocity field that generates a flow given by ψ t,h (p) which is the location at time t + h of a point that at time t is at p. Such a flow is incorporated into a stochastic framework by means of the stochastic integral…”

Section: 3mentioning

confidence: 99%

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Dynamically evolving Gaussian spatial fields

2010

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Abstract. We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields and by applying an extension of the standard moving average construction we arrive to stationary in time models. The obtained surface although changing in time can be considered dynamically inactive since its velocities when sampled across the field have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models that are extensions of the previous discretized auto-regressions accounting for a local velocity of traveling surface. For such a surface we demonstrate that its dynamics is a combination of dynamics introduced by the flow and the dynamics resulting from the covariance structure of the underlying stochastic field. We extend this approach to fields that are only locally stationary and have their parameters varying over a larger spatio-temporal horizon.

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Section: 3mentioning

confidence: 99%

“…The generality of the approach allows a natural extension for second order models that goes beyond Gaussian distribution but this is not explored here. Steps in this direction have been undertaken for the fields driven by Laplace motion in [1] and will be continued in future research.…”

Section: 3mentioning

confidence: 99%

Dynamically evolving Gaussian spatial fields

2010

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“…The Laplace moving average field was introduced inÅberg and Podgórski (2011). It can be also constructed using Eq.…”

Section: Laplace Moving Average Model (Lma) X Lmamentioning

confidence: 99%

Spatio-temporal modelling of wind speed variations and extremes in the Caribbean and the Gulf of Mexico

Rychlik

Mao

2018

Theor Appl Climatol

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The wind speed variability in the North Atlantic has been successfully modelled using a spatio-temporal transformed Gaussian field. However, this type of model does not correctly describe the extreme wind speeds attributed to tropical storms and hurricanes. In this study, the transformed Gaussian model is further developed to include the occurrence of severe storms. In this new model, random components are added to the transformed Gaussian field to model rare events with extreme wind speeds. The resulting random field is locally stationary and homogeneous. The localized dependence structure is described by time-and space-dependent parameters. The parameters have a natural physical interpretation. To exemplify its application, the model is fitted to the ECMWF ERA-Interim reanalysis data set. The model is applied to compute longterm wind speed distributions and return values, e.g., 100-or 1000-year extreme wind speeds, and to simulate random wind speed time series at a fixed location or spatio-temporal wind fields around that location.

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“…The significance of AL distributions, denoted by AL d ( , µ), is partially due to fact that these arise rather naturally as the only distributional limits for (appropriately normalized) random sums X (1) + · · · + X (N p )…”

Section: Introductionmentioning

confidence: 99%

Multivariate generalized Laplace distribution and related random fields

Kozubowski

Podgórski

Rychlik

2013

Journal of Multivariate Analysis

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a b s t r a c tMultivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments. A Lévy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. We review their basic properties and discuss a construction of a class of moving average vector processes driven by multivariate Laplace motion. These stochastic models extend to vector fields, which are multivariate both in the argument and the value. They provide an attractive alternative to those based on Gaussianity, in presence of asymmetry and heavy tails in empirical data. An example from engineering shows modeling potential of this construction.

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A class of non-Gaussian second order random fields

Cited by 30 publications

References 20 publications

Dynamically evolving Gaussian spatial fields

Dynamically evolving Gaussian spatial fields

Spatio-temporal modelling of wind speed variations and extremes in the Caribbean and the Gulf of Mexico

Multivariate generalized Laplace distribution and related random fields

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