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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 .