Stationary and self-similar processes driven by Lévy processes

Ole Barndorff-Nielsen and Victor Pérez-Abreu

Stochastic Processes and their Applications, 1999, vol. 84, issue 2, 357-369

Abstract: Using bivariate Lévy processes, stationary and self-similar processes, with prescribed one-dimensional marginal laws of type G, are constructed. The self-similar processes are obtained from the stationary by the Lamperti transformation. In the case of square integrability the arbitrary spectral distribution of the stationary process can be chosen so that the corresponding self-similar process has second-order stationary increments. The spectral distribution in question, which yields fractional Brownian motion when the driving Lévy process is the bivariate Brownian motion, is shown to possess a density, and an explicit expression for the density is derived.

Keywords: Fractal; spectral; density; Normal; inverse; Gaussian; Second-order; stationary; increments; Type; G (search for similar items in EconPapers)
Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00061-7
Full text for ScienceDirect subscribers only

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:eee:spapps:v:84:y:1999:i:2:p:357-369

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().