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# New classes of self-similar symmetric stable
random fields

**Piotr S. Kokoszka
**

Murad S. Taqqu

### Abstract:

*We construct two new classes of symmetric stable
self-similar
random fields with stationary increments, one of the moving average
type, the other of the harmonizable type. The fields are defined
through an integral representation whose kernel involves a
norm on . We examine how the choice of the norm affects the
finite-dimensional distributions. We also study the processes which
are obtained by projecting the random fields on a one-dimensioanl
subspace. We compare these
`projection processes'
with each other and with other well-known self-similar
processes and we characterize their asymptotic dependence structure.
*