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Title: Spatial-temporal stochastic fields with embedded dynamics Authors:  Krzysztof Podgorski - Lund University (Sweden) [presenting]
Abstract: General non-stationary spatial-temporal surfaces that involve dynamics governed by velocity fields are discussed. In that approach, the dynamics are introduced by embedding deterministic velocities into a stochastic spatial-temporal Gaussian model. In this way, a dynamically inactive stochastic field with a given spatial and temporal covariance structure gains dynamics that in general follow a deterministic pattern. We make an important connection between the resulting stochastic field and underlying deterministic dynamics by demonstrating that in the case of isotropic spatial dependencies, the observed random velocities are centered at the velocities of the underlying physical flow. Additionally, we discuss strategies for simulation of such fields and give a foundation for statistical fitting and prediction procedures that are based on the obtained results.