Holomorphic transforms with application to affine processes
Please always quote using this URN:urn:nbn:de:0296-matheon-4676
- 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.
Author: | Denis Belomestny, Joerg Kampen, John Schoenmakers |
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URN: | urn:nbn:de:0296-matheon-4676 |
Referee: | Peter Imkeller |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2008/02/26 |
Release Date: | 2008/02/26 |
Preprint Number: | 458 |