Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes

Abstract:

Constructing Levy-driven Ornstein-Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will be hereafter called the a-remainder of their self-decomposable stationary laws. In the present study we fully characterize the Levy triplet of these a-remainders and we provide a general framework to deduce the transition laws of the finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions. We focus finally on the subclass of the exponentially-modulated tempered stable laws and we derive the algorithms for an exact generation of the skeleton of Ornstein-Uhlenbeck processes related to such distributions, with the further advantage of adopting a procedure computationally more efficient than those already available in the existing literature. The talk is based on a joint work with Prof. Nicola Cufaro Petroni.

Organizzatore:

Alberto Lanconelli