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The asymptotic dependence structure of the linear fractional Lévy
Joshua B. Levy
Murad S. Taqqu
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
<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 .