# Field functions¶

A field function where and is defined by:

(1)¶

with and . A field function transforms a multivariate stochastic process:

where is discretized according to the into the multivariate stochastic process:

such that:

where the mesh is discretized according to the .

A field function also acts on fields and produces
fields of possibly different dimension () and mesh
( or ).

**Value function**

A value function
is
a particular field function that lets invariant the mesh of a
field and defined by a function
such that:

(2)¶

Let’s note that the input dimension of still designs
the dimension of : . Its output dimension is
equal to .

The creation of a value function requires the
function and the integer : the
dimension of the vertices of the mesh . This data is
required for tests on the compatibility of dimension when a composite
process is created using the value function.

**Vertex value function**

A vertex-value function
is
a particular field function that lets invariant the mesh of a
field and defined by a function
such that:

(3)¶

Let’s note that the input dimension of still design
the dimension of : . Its output dimension is
equal to .