Asymptotic behaviour of the distribution density of the fractional Lévy motion

Victoria Knopova; Alexei Kulik

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arXiv · 1112.0497

Asymptotic behaviour of the distribution density of the fractional Lévy motion

Victoria Knopova·Alexei Kulik

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Abstract

We investigate the distribution properties of the fractional Lévy motion. We consider separately the cases $0<H<1/2$ (short memory) and $1/2<H<1$ (long memory), where $H$ is the Hurst parameter, and present the asymptotic behaviour of the distribution density of the process. Some examples are provided, in which it is shown that the behaviour of the density in the cases $0<H<1/2$ and $1/2<H<1$ is completely different.

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Victoria Knopova, Alexei Kulik. 2013-08-08. Asymptotic behaviour of the distribution density of the fractional Lévy motion. https://arxiv.org/abs/1112.0497

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