1. Discretization and calculation methods

1.1 Discretization of random fields

The discretization of random fields transforms the individual fields into vectors of correlated random variables.

Let ν(x) be a multidimensional random field defined in a domain Ω. The field is considered to be completely described by its meanE(x), its varianceσ ² (x) and its correlation functionρ(x, x') between two distinct points with coordinates x and x'. Discretizing the fieldv(x) involves replacing it with a random vector v. All existing methods relate v(x) to v, using a linear transformation, so for a Gaussian random field, v is also Gaussian.

There are numerous methods for discretizing random fields