Geodesic
Uniqueness of the inverse first-passage time problem and the shape of the Shiryaev boundary
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 717-744

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

Given a distribution on the positive extended real line, the two-sided inverse first-passage time problem for Brownian motion asks for a function such that the first passage time of this function by a reflected Brownian motion has the given distribution. We combine the ideas of Ekström and Janson, which were developed within the scope of the one-sided inverse first-passage time problem, with the methods of De Masi et al., which were used in the context of free boundary problems, in order to give a different proof for the uniqueness for the two-sided inverse first-passage time problem by using a stochastic order relation. We provide criteria for qualitative properties of solutions of the inverse first-passage problem, which apply to the boundary corresponding to the exponential distribution.
Keywords: inverse first-passage time, Brownian motion, Shiryaev problem, boundary crossing. 
@article{TVP_2022_67_4_a4,
     author = {A. Klump and M. Kolb},
     title = {Uniqueness of the inverse first-passage time problem and the shape of the {Shiryaev} boundary},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {717--744},
     publisher = {mathdoc},
     volume = {67},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a4/}
}
TY  - JOUR
AU  - A. Klump
AU  - M. Kolb
TI  - Uniqueness of the inverse first-passage time problem and the shape of the Shiryaev boundary
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2022
SP  - 717
EP  - 744
VL  - 67
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a4/
LA  - ru
ID  - TVP_2022_67_4_a4
ER  - 
%0 Journal Article
%A A. Klump
%A M. Kolb
%T Uniqueness of the inverse first-passage time problem and the shape of the Shiryaev boundary
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2022
%P 717-744
%V 67
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a4/
%G ru
%F TVP_2022_67_4_a4
A. Klump; M. Kolb. Uniqueness of the inverse first-passage time problem and the shape of the Shiryaev boundary. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 717-744. http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a4/