A Mixed Limit Theorem for Stable Random Fields

A mixed distributional limit theorem for a stable random field of index 0 < [alpha] > 2 is derived. These random fields are of special interest in pattern analysis, in particular, in pattern synthesis. This paper considers the ease when the underlying graph that the random field is defined on is linear. This result is encouraging insofar as it shows that the mixed limit theorems do exist in the stable case. The final limiting distribution can be written in terms of the stable process of index [alpha] in D[0, 1].