TY - JOUR
T1 - On a formula on the potential operators of absorbing Lévy processes in the half space
AU - Tamura, Yozo
AU - Tanaka, Hiroshi
N1 - Funding Information:
Yozo Tamura was partially supported by Grant-in Aid for Scientific Research(17540133) MEXT, Japan.
PY - 2008/2
Y1 - 2008/2
N2 - A representation of the potential operator of an absorbing Lévy process in the half space (0, ∞) × Rd - 1, d ≥ 2, is given in terms of three measures μ, over(μ, ̂) and over(μ, ̇) on [0, ∞) × Rd - 1 arising in the fluctuation theory of Lévy processes. In the case of a rotation invariant stable Lévy process, the potential kernel in the half space is computed explicitly. It will also be proved that the measure over(μ, ̂) is an excessive measure (an invariant measure under some conditions) of a Markov process, which is derived from the given Lévy process in a certain way.
AB - A representation of the potential operator of an absorbing Lévy process in the half space (0, ∞) × Rd - 1, d ≥ 2, is given in terms of three measures μ, over(μ, ̂) and over(μ, ̇) on [0, ∞) × Rd - 1 arising in the fluctuation theory of Lévy processes. In the case of a rotation invariant stable Lévy process, the potential kernel in the half space is computed explicitly. It will also be proved that the measure over(μ, ̂) is an excessive measure (an invariant measure under some conditions) of a Markov process, which is derived from the given Lévy process in a certain way.
KW - Absorbing Lévy process
KW - Fluctuation theory
KW - Lévy process
KW - Potential operator
KW - Rotation invariant stable Lévy process
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U2 - 10.1016/j.spa.2007.04.005
DO - 10.1016/j.spa.2007.04.005
M3 - Article
AN - SCOPUS:37249003706
VL - 118
SP - 199
EP - 212
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 2
ER -