Dynamically Evolving Gaussian Spatial Fields
Preprint, 2008

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.

spectral density

velocity field

covariance function

stationary second order processes


Anastassia Baxevani

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematisk statistik

Krzysztof Podgórski

Igor Rychlik

Chalmers, Matematiska vetenskaper, Matematisk statistik

Göteborgs universitet


Sannolikhetsteori och statistik

Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University: 2008:46

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