Fractal dimensions of rough differential equations driven by fractional Brownian motions

Shuwen Lou and Cheng Ouyang

Stochastic Processes and their Applications, 2016, vol. 126, issue 8, 2410-2429

Abstract: In this work we study fractal properties of a d-dimensional rough differential equation driven by fractional Brownian motions with Hurst parameter H>14. In particular, we show that the Hausdorff dimension of the sample paths of the solution is min{d,1H} and that the Hausdorff dimension of the level set Lx={t∈[ϵ,1]:Xt=x} is 1−dH with positive probability when dH<1.

Keywords: Fractional Brownian motion; Fractal dimension; Sample path; Level set (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414916000375
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:126:y:2016:i:8:p:2410-2429

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

DOI: 10.1016/j.spa.2016.02.005

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 ().