Spectral analysis of subordinate Brownian motions on the half-line

Mateusz Kwaśnicki. "Spectral analysis of subordinate Brownian motions on the half-line." Studia Mathematica 206.3 (2011): 211-271. <http://eudml.org/doc/285702>.

@article{MateuszKwaśnicki2011,
abstract = {We study one-dimensional Lévy processes with Lévy-Khintchine exponent ψ(ξ²), where ψ is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators whose Lévy measure has completely monotone density; or, equivalently, symmetric Lévy processes whose Lévy measure has completely monotone density on (0,∞). Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition operators of the process killed after exiting the half-line. A generalized eigenfunction expansion of the transition operators is derived. As an application, a formula for the distribution of the first passage time (or the supremum functional) is obtained.},
author = {Mateusz Kwaśnicki},
journal = {Studia Mathematica},
keywords = {Lévy process; subordination; Wiener-Hopf factorization; complete Bernstein function; completely monotone function; killed process; spectral theory; first passage time},
language = {eng},
number = {3},
pages = {211-271},
title = {Spectral analysis of subordinate Brownian motions on the half-line},
url = {http://eudml.org/doc/285702},
volume = {206},
year = {2011},
}

TY - JOUR
AU - Mateusz Kwaśnicki
TI - Spectral analysis of subordinate Brownian motions on the half-line
JO - Studia Mathematica
PY - 2011
VL - 206
IS - 3
SP - 211
EP - 271
AB - We study one-dimensional Lévy processes with Lévy-Khintchine exponent ψ(ξ²), where ψ is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators whose Lévy measure has completely monotone density; or, equivalently, symmetric Lévy processes whose Lévy measure has completely monotone density on (0,∞). Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition operators of the process killed after exiting the half-line. A generalized eigenfunction expansion of the transition operators is derived. As an application, a formula for the distribution of the first passage time (or the supremum functional) is obtained.
LA - eng
KW - Lévy process; subordination; Wiener-Hopf factorization; complete Bernstein function; completely monotone function; killed process; spectral theory; first passage time
UR - http://eudml.org/doc/285702
ER -