Unilateral small deviations of processes related to the fractional Brownian motion

G. Molchan

Stochastic Processes and their Applications, 2008, vol. 118, issue 11, 2085-2097

Abstract: Let x(s), s[set membership, variant]Rd be a Gaussian self-similar random process of index H. We consider the problem of log-asymptotics for the probability pT that x(s), x(0)=0 does not exceed a fixed level in a star-shaped expanding domain T[dot operator][Delta] as T-->[infinity]. We solve the problem of the existence of the limit, [theta]:=lim(-logpT)/(logT)D, T-->[infinity], for the fractional Brownian sheet x(s), s[set membership, variant][0,T]2 when D=2, and we estimate [theta] for the integrated fractional Brownian motion when D=1.

Keywords: Small; deviations; Fractional; Brownian; motion; Level; crossing; probability (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(07)00203-7
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:118:y:2008:i:11:p:2085-2097

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 ().