Holomorphic transforms with application to affine processes (Q2391274)

In the general setting of Itô-Lévy processes, the authors study a class of transforms, e.g., Fourier, of the state variable of a process, which are holomorphic in some disc around zero in the complex plane. It is shown that such transforms are related to a system of analytic vectors for the generator of the process. Conditions are given allowing for holomorphic extension of these transforms into a strip which contains the positive real axis. Based on them, the authors develop a functional series expansion of the transforms in terms of the constituents of the generator. As an application, it is shown 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. Log-affine series representations for the transform are also given.