Lévy Measure Density Corresponding to Inverse Local Time

We are concerned with the L évy measure density corresponding to the inverse local time at the regular end point for a harmonic transform of a one-dimensional di usion process. We show that the L evy measure density is represented as the Laplace transform of the spectral measure corresponding to the...

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Veröffentlicht in:Publications of the Research Institute for Mathematical Sciences 2013, Vol.49 (3), p.563-599
Hauptverfasser: Takemura, Tomoko, Tomisaki, Matsuyo
Format: Artikel
Sprache:eng
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Zusammenfassung:We are concerned with the L évy measure density corresponding to the inverse local time at the regular end point for a harmonic transform of a one-dimensional di usion process. We show that the L evy measure density is represented as the Laplace transform of the spectral measure corresponding to the original di usion process, where the absorbing boundary condition is posed at the end point whenever it is regular.
ISSN:0034-5318
1663-4926
DOI:10.4171/PRIMS/113