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# The asymptotic dependence structure of the linear fractional Lévy
motion

**A. Astrauskas
**

Joshua B. Levy

Murad S. Taqqu

### Abstract:

*Let be the linear fractional Lévy motion,
that is, an -stable H-self-similar process with stationary increments,
parametrized by and ***0<H<1**, , and possessing a moving-average type representation. Let be the increment
process. The asymptotic dependence structure of the stationary process
can be measured
for real and by , as .
It is shown that , , where and . For example, if , then
if
**<H<1**, but if . These results extend initial work of Astrauskas (1984).
The behavior of is also studied for the
stationary increments of Log-fractional Lévy motion, an -stable
-self-similar process defined for .