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# Asymptotic dependence of moving average type self-similar
stable random fields

**Piotr S. Kokoszka
**

Murad S. Taqqu

### Abstract:

*We investigate the asymptotic dependence structure of
a large class of self-similar stable random fields which are
extensions of the linear fractional Lévy motion to the parameter
space . The dependence is measured through the difference of
the joint characteristic function and the product of the marginal
characteristic functions.
We show that the intensity of the dependence
decreases to zero like a power function as the lag
tends to infinity and we obtain
the exact expression for the exponent in the power function. The
exponent
depends on both the stability parameter and the self-similarity parameter.
*