Stein's non-separable space-time model
RMstein is a univariate stationary covariance model
whose corresponding covariance function only depends on the difference
h between two points and is given by
C(h, t) = W_ν(y) - < h, z > t W_{ν-1}(y) / [ (ν-1) (2ν + d + 1) ]
Here, W_ν is the covariance of the
RMwhittle model with
smoothness parameter ν;
y = ||(h,t)|| is the norm of the vector
(h,t),
d is the dimension of the space on which the random field is considered.
RMstein(nu, z, var, scale, Aniso, proj)
nu |
numerical value; greater than 1; smoothness parameter of the RMwhittle model |
z |
a vector; the norm of z must be less or equal to 1. |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
See Stein (2005).
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Stein, M.L. (2005) Space-time covariance functions. J. Amer. Statist. Assoc. 100, 310-321. Equation (8).
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again model <- RMstein(nu=1.5, z=0.9) x <- seq(0, 10, 0.05) plot(RFsimulate(model, x=x, y=x))
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