实值多分数Lévy过程的样本轨道性质（英文）

Some sample path properties of real multifractional Lévy processes

通过把分数Lévy过程中Hurst指标H替换成局部的β-Hlder函数的方法,定义实值多分数Lévy过程,它可以看作多分数布朗运动和实值分数Lévy过程的推广,但该过程不再是平稳增量过程。证明实值多分数Lévy过程的二阶矩可以被局部的β-Hlder函数控制,该过程是局部自相似的,给出它的渐近行为。

Real multifractional Levy process （RMLP） is defined by substituting the Hurst parameter H （0,1） to a HOlder function H（t） ∈ （0,1） in the definition of fractional Levy process. RMLP is the gen- eralization of the multifractional Brownian motion and of the real fractional Levy process, but it is not a stationary increment. It is shown that RMLP＇ s second-order moment can be controlled by locally β- Holder function, it is a locally self-similar process and gives an asymptotical behavior of RMLP.