Potential theory of one-dimensional geometric stable processes

Tomasz Grzywny, and Michał Ryznar. "Potential theory of one-dimensional geometric stable processes." Colloquium Mathematicae 129.1 (2012): 7-40. <http://eudml.org/doc/283793>.

@article{TomaszGrzywny2012,
abstract = {The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter α ∈ (0,2]. This process has an infinitesimal generator of the form $-log(1+(-Δ)^\{α/2\})$. As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.},
author = {Tomasz Grzywny, Michał Ryznar},
journal = {Colloquium Mathematicae},
keywords = {potential theory; one-dimensional geometric stable processes; Harnack inequality},
language = {eng},
number = {1},
pages = {7-40},
title = {Potential theory of one-dimensional geometric stable processes},
url = {http://eudml.org/doc/283793},
volume = {129},
year = {2012},
}

TY - JOUR
AU - Tomasz Grzywny
AU - Michał Ryznar
TI - Potential theory of one-dimensional geometric stable processes
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 1
SP - 7
EP - 40
AB - The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter α ∈ (0,2]. This process has an infinitesimal generator of the form $-log(1+(-Δ)^{α/2})$. As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.
LA - eng
KW - potential theory; one-dimensional geometric stable processes; Harnack inequality
UR - http://eudml.org/doc/283793
ER -