The stochastic delay differential equationis considered, where Z(t) is a process with independent stationary increments and a is a finite signed measure. We obtain necessary and sufficient conditions for the existence of a stationary solution to this equation in terms of a and the Lévy measure...

We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations...

We present a class of Lévy processes for modelling financial market fluctuations: bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an...