Holomorphic transforms with application to affine processes
In a rather general setting of Itô-Lévy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generat...
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| Sprache: | eng |
| Veröffentlicht: |
Berlin
WIAS
2008
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| Schriftenreihe: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik
1297 |
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Tag hinzufügen | Zusammenfassung: | In a rather general setting of Itô-Lévy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generator of the process, and we state conditions which allow for holomorphic extension of these transforms into a strip which contains the positive real axis. Based on these extensions we develop a functional series expansion of these transforms in terms of the constituents of the generator. As application, we show that for multidimensional affine Itô-Lévy processes with state dependent jump part the Fourier transform is holomorphic in a time strip under some stationarity conditions, and give log-affine series representations for the transform. |
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| Beschreibung: | 25 S. |