Asymptotic Behaviour of the Distribution Density of the Fractional Lévy Motion

Victoria P. Knopova () and Alexey M. Kulik ()
Additional contact information
Victoria P. Knopova: Ukrainian National Academy of Sciences
Alexey M. Kulik: Ukrainian National Academy of Sciences

A chapter in Modern Stochastics and Applications, 2014, pp 175-201 from Springer

Abstract: Abstract We investigate the distribution properties of the fractional Lévy motion defined by the Mandelbrot-Van Ness representation: $$\displaystyle{Z_{t}^{H}:=\int _{ \mathbb{R}}f(t,s)dZ_{s},}$$ where Z s , $$s \in \mathbb{R}$$ , is a (two-sided) real-valued Lévy process, and $$\displaystyle{f(t,s):= \frac{1} {\varGamma (H + 1/2)}\left [(t - s)_{+}^{H-1/2} - (-s)_{ +}^{H-1/2}\right ],\quad t,s \in \mathbb{R}.}$$ We consider separately the cases 0

Keywords: Asymptotic Behaviour; Distribution Density; Inverse Fourier Transform; Fractional Brownian Motion; Distribution Property (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-03512-3_11

Ordering information: This item can be ordered from
http://www.springer.com/9783319035123

DOI: 10.1007/978-3-319-03512-3_11

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().