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Dynamically evolving Gaussian spatial fields

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Author

Summary, in English

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. By applying an extension of the standard moving average construction we obtain models which are stationary in time. The resulting surface changes with time but is 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. The models are extensions of the earlier discretized autoregressive models which account for a local velocity of traveling surface. We demonstrate that for such a surface 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.

Publishing year

2011

Language

English

Pages

223-251

Publication/Series

Extremes

Volume

14

Issue

2

Document type

Journal article

Publisher

Springer

Topic

  • Probability Theory and Statistics

Keywords

  • Spectral density
  • Covariance function
  • Stationary second order
  • processes
  • Velocity field

Status

Published

ISBN/ISSN/Other

  • ISSN: 1572-915X