Stochastic calculus for convoluted Levy processes

We develop a stochastic calculus for processes which are built by convoluting a pure jump, zero expectation Levy process with a Volterra-type kernel. This class of processes contains, for example, fractional Levy processes as studied by Marquardt [Bernoulli 12 (2006) 1090-1126.] The integral which we introduce is a Skorokhod 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 Ito formula which separates the different contributions from the memory due to the convolution and from the jumps.