On the supremum of gamma-reflected processes with fractional Brownian motion as input
Details
State: Public
Version: author
Serval ID
serval:BIB_28B3A7E8CADC
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
On the supremum of gamma-reflected processes with fractional Brownian motion as input
Journal
Stochastic Processes and their Applications
ISSN
0304-4149 (Print)
Publication state
Published
Issued date
2013
Peer-reviewed
Oui
Volume
123
Number
11
Pages
4111-4127
Language
english
Abstract
Let {X-H(t), t >= 0} be a fractional Brownian motion with Hurst index H is an element of (0, 1] and define a gamma-reflected process W-gamma(t) = X-H(t) - ct - gamma inf(s is an element of[0,t])(X-H(s) - cs), t >= 0 with c > 0, gamma is an element of [0, 1] two given constants. In this paper we establish the exact tail asymptotic behaviour of M-gamma(T) = sup(t is an element of[0,T]) W-gamma(t) for any T is an element of (0, infinity]. Furthermore, we derive the exact tail asymptotic behaviour of the supremum of certain non-homogeneous mean-zero Gaussian random fields.
Keywords
Gamma-reflected process, Fractional Brownian motion, Supremum, Exact asymptotics, Ruin probability, Extremes of Gaussian random fields
Web of science
Create date
11/06/2013 20:42
Last modification date
20/08/2019 14:08