Volterra-Lévy过程的重分形性质
The Multifractal Nature of Volterra-Lévy Processes
摘要：
本文研究了Volterra-Lévy过程样本路径的正则性。这些过程被定义为随机积分$$ M(t)=\int_{0}^{t}F(t,r)dX(r), \ \ t \in \mathds{R}_{+}, $$，其中$X$是Lévy过程，$F$是确定性实值函数。我们得到的频谱的奇异性和结果的2-微局部前沿的$\{M(t)\}_{t\in [0,1]}$，正则性假设下的功能$F$。
英文摘要：
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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