Holomorphic transforms with application to affine processes
| dc.creator | Belomestny, D. | |
| dc.creator | Kampen, J. | |
| dc.creator | Schoenmakers, J. | |
| dc.date | 2008-07-08 | |
| dc.date.accessioned | 2026-07-07T09:49:07Z | |
| dc.date.available | 2026-07-07T09:49:07Z | |
| dc.description | 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. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0807.1289 | |
| dc.identifier | http://arxiv.org/abs/0807.1289 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164466 | |
| dc.subject | Functional Analysis | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 60J25, 91B28 | |
| dc.title | Holomorphic transforms with application to affine processes | |
| dc.type | text |