Reflecting L\'evy processes and associated families of linear operators
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 417-441
Voir la notice de l'article provenant de la source Math-Net.Ru
The paper is concerned with special one-dimensional Markov processes, which
are Lévy processes defined on a finite interval and reflected
from the boundary points of the interval. It is shown that in this setting,
in addition to the standard semigroup of operators generated by the Markov
process, there also appears the family of “boundary” random operators that
send functions defined on the boundary of the interval to elements of the
space $L_2$ on the entire interval. In the case when the original process is
a Wiener process, we show that these operators can be expressed in terms of
the local time of the process on the boundary of the interval.
Keywords:
random process, initial boundary value problem, limit theorem, local time.
@article{TVP_2019_64_3_a0,
author = {I. A. Ibragimov and N. V. Smorodina and M. M. Faddeev},
title = {Reflecting {L\'evy} processes and associated families of linear operators},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {417--441},
publisher = {mathdoc},
volume = {64},
number = {3},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a0/}
}
TY - JOUR AU - I. A. Ibragimov AU - N. V. Smorodina AU - M. M. Faddeev TI - Reflecting L\'evy processes and associated families of linear operators JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2019 SP - 417 EP - 441 VL - 64 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a0/ LA - ru ID - TVP_2019_64_3_a0 ER -
%0 Journal Article %A I. A. Ibragimov %A N. V. Smorodina %A M. M. Faddeev %T Reflecting L\'evy processes and associated families of linear operators %J Teoriâ veroâtnostej i ee primeneniâ %D 2019 %P 417-441 %V 64 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a0/ %G ru %F TVP_2019_64_3_a0
I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. Reflecting L\'evy processes and associated families of linear operators. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 417-441. http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a0/