The Multifractal Nature of Volterra-L\'{e}vy Processes

We consider the regularity of sample paths of Volterra-L'{e}vy processes. These processes are defined as stochastic integrals $$M(t)={\int }_0^{t}F(t,r)dX(r),t\in \text{mathds}{R}_{+},$$ where $X$ is a L'{e}vy process and $F$ is a deterministic real-valued function. We derive the spectrum of singularities and a result on the 2-microlocal frontier of $\{M(t){\}}_{t\in [0,1]}$, under regularity assumptions on the function $F$.