Holomorphic Transforms with Application to Affine Processes

Denis Belomestny, Joerg Kampen, John Schoenmakers
2008 Social Science Research Network  
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
more » ... e develop a functional series expansion of these transforms in terms of the constituents of the generator. As application, we show that for multi-dimensional 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.
doi:10.2139/ssrn.1090858 fatcat:zdazdd4dmnbtpmphb2ukpaysj4