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The talk introduces a new class of random fields, supCAR fields, which
are constructed as superpositions of continuous autoregressive random
fields. These supCAR fields possess infinitely divisible marginal
distributions. Their second-order properties are characterised by a
novel family of covariance functions that allows both short- and
long-range spatial dependencies. Functional limit theorems for supCAR
fields are derived under general assumptions. Four limiting scenarios
that depend on the marginals of the underlying autoregressive fields and
the specifications of the superposition are identified. The obtained
limit theorems can be employed for the statistical inference of supCAR
fields.