Stochastic calculus for convoluted Lévy processes

We develop a stochastic calculus for processes which are built by convoluting a pure jump, zero expectation Lévy process with a Volterra-type kernel. This class of processes contains, for example, fractional Lévy processes as studied in Marquardt (2006b). The integral which we introduce is a Skorohod integral. Nonetheless we avoid the technicalities from Malliavin calculus and white noise analysis, and give an elementary definition based on expectations under change of measure. As a main result we derive an Itô formula, which separates the different contributions from the memory due to the convolution and from the jumps.     «

We develop a stochastic calculus for processes which are built by convoluting a pure jump, zero expectation Lévy process with a Volterra-type kernel. This class of processes contains, for example, fractional Lévy processes as studied in Marquardt (2006b). The integral which we introduce is a Skorohod integral. Nonetheless we avoid the technicalities from Malliavin calculus and white noise analysis, and give an elementary definition based on expectations under change of measure. As a main result...     »