Brown, Patrick E.; Kåresen, Kjetil F.; Roberts, Gareth O.; Tonellato, Stefano Blur-generated non-separable space-time models. (English) Zbl 0957.62081 J. R. Stat. Soc., Ser. B, Stat. Methodol. 62, No. 4, 847-860 (2000). Summary: Statistical space-time modelling has traditionally been concerned with separable covariance functions, meaning that the covariance function is a product of a purely temporal function and a purely spatial function. We draw attention to a physical dispersion model which could model phenomena such as the spread of an air pollutant. We show that this model has a non-separable covariance function. The model is well suited to a wide range of realistic problems which will be poorly fitted by separable models. The model operates successively in time: the spatial field at time \(t+1\) is obtained by ‘blurring’ the field at time \(t\) and adding a spatial random field.The model is first introduced at discrete time steps, and the limit is taken as the length of the time steps goes to 0. This gives a consistent continuous model with parameters that are interpretable in continuous space and independent of sampling intervals. Under certain conditions the blurring must be a Gaussian smoothing kernel. We also show that the model is generated by a stochastic differential equation which has been studied by several researchers previously. Cited in 41 Documents MSC: 62M30 Inference from spatial processes 62P35 Applications of statistics to physics Keywords:continuous time; infinitely divisible functions; partial stochastic differential equation; Ornstein-Uhlenbeck process; blurring PDFBibTeX XMLCite \textit{P. E. Brown} et al., J. R. Stat. Soc., Ser. B, Stat. Methodol. 62, No. 4, 847--860 (2000; Zbl 0957.62081) Full Text: DOI