Geodesic
Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 100-114

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the persistence probability for the integrated fractional Brownian motion and the fractionally integrated Brownian motion with parameter $H$, respectively. For the integrated fractional Brownian motion, we discuss a conjecture of Molchan and Khokhlov and determine the asymptotic behavior of the persistence exponent as $H\to 0$ and $H\to 1$, which is in accordance with the conjecture. For the fractionally integrated Brownian motion, also called the Riemann–Liouville process, we find the asymptotic behavior of the persistence exponent as $H\to 0$.
Keywords: Gaussian process, integrated fractional Brownian motion, one-sided exit problem, stationary process, zero crossing.
Mots-clés : persistence, Riemann–Liouville process 
@article{TVP_2022_67_1_a5,
     author = {F. Aurzada and M. Kilian},
     title = {Asymptotics of the persistence exponent of integrated fractional {Brownian} motion and fractionally integrated {Brownian} motion},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {100--114},
     publisher = {mathdoc},
     volume = {67},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a5/}
}
TY  - JOUR
AU  - F. Aurzada
AU  - M. Kilian
TI  - Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2022
SP  - 100
EP  - 114
VL  - 67
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a5/
LA  - ru
ID  - TVP_2022_67_1_a5
ER  - 
%0 Journal Article
%A F. Aurzada
%A M. Kilian
%T Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2022
%P 100-114
%V 67
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a5/
%G ru
%F TVP_2022_67_1_a5
F. Aurzada; M. Kilian. Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 100-114. http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a5/