The multifractal nature of Volterra-Lévy processes

We consider the regularity of sample paths of Volterra-Lévy processes. These processes are defined as stochastic integrals M(t)=∫0tF(t,r)dX(r),t∈R+, where X is a Lévy process and F is a deterministic real-valued function. We derive the spectrum of singularities and a result on the 2-microlocal frontier of {M(t)}t∈[0,1], under regularity assumptions on the function F.