Generalized Conjugate Processes: Lévy Diffusions and Financial Applications

Eduardo Horta

We consider sequences of Lévy Diffusions driven by a latent, discrete time state (possibly infinite dimensional). The proposed model is a generalization of methodology developed by Horta and Ziegelmann (Stochastic Processes and Applications, 2018, 128, 727-755). We show that the usual approach of estimating the covariance operator of the diffusion entails difficulties in this framework, and propose an alternative based on the functional Fourier transform. Asymptotic results are derived, and the theory is illustrated by an application to financial data.