The Multifractal Nature of Volterra-Lévy Processes

Abstract: We consider the regularity of sample paths of Volterra-L\'{e}vy processes. These processes are defined as stochastic integrals $$ M(t)=\int_{0}^{t}F(t,r)dX(r), \ \ t \in \mathds{R}{+}, $$ 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 $F$.