Definition
A random function is a type of random element in which a single outcome is selected from some family of functions, where the family consists some class of all maps from the domain to the codomain. For example the class may be restricted to all continuous functions or to all step function. The values determined by a random function evaluated at different points from the same realization would not generally be statistically independent but, depending on the model, values deterimined at the same or different points from different realisations might well be treated as independent.
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