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arXiv · 1306.3595

The Multifractal Nature of Volterra-Lévy Processes

Eyal Neuman
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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 $F$.

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Eyal Neuman. 2014-05-19. The Multifractal Nature of Volterra-Lévy Processes. https://doi.org/10.1016/j.spa.2014.04.011

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