Generalized fractional Laplace motion

J. Gajda, A. Wyłomańska and A. Kumar

Statistics & Probability Letters, 2017, vol. 124, issue C, 101-109

Abstract: In this paper, a new stochastic process called generalized fractional Laplace motion (GFLM) is introduced. This process is obtained by superposition of nth-order fractional Brownian motion (n-FBM) as outer process and gamma process as inner process. It is shown that n-FBM process has long-range-dependence (LRD), persistence of signs LRD and persistence of magnitudes LRD properties. Distributional properties of GFLM such as probability density function, moments, covariance structure are established. The fractional partial differential equation governed by the GFLM density is obtained. Finally, it is shown that GFLM has LRD property for all H∈(n−1,n), similar to the n-FBM case.

Keywords: Fractional Brownian motion; Gamma process; Subordination (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715217300366
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:stapro:v:124:y:2017:i:c:p:101-109

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

DOI: 10.1016/j.spl.2017.01.013

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().