The Multifractal Nature of Volterra-Lévy Processes

Abstract

We consider the regularity of sample paths of Volterra-Lévy 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 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 $\{M(t){\}}_{t\in [0,1]}$, under regularity assumptions on the function $F$.

21 pages, Stochastic Processes and their Applications, 2014

References in corpus (2)

• Fine regularity of Lévy processes and linear (multi)fractional stable motion
• A generalised Itō formula for Lévy-driven Volterra processes

Cited by in corpus (2)

• Uniform multifractal structure of stable trees
• A generalised Itō formula for Lévy-driven Volterra processes