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 ) = ∫ 0 t F ( t , r ) d X ( 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 .