论文标题
Rosenblatt过程的当地时间和样本路径属性
Local times and sample path properties of the Rosenblatt process
论文作者
论文摘要
令$ z =（z_t）_ {t \ geq 0} $为hurst index $ h \ in（1/2，1）$的rosenblatt进程。我们证明了$ z $的当地时代的联合连续性，并在当地时代建立了Hölder条件。然后，这些结果用于研究$ z $的样本路径的不规则性。基于分数布朗运动的类比，我们认为我们的结果很清晰。我们证明的主要成分是对整体运算符的任意线性组合的相当微妙的光谱分析，这是由Rosenblatt过程作为第二个混乱中的元素而产生的。
Let $Z = (Z_t)_{t \geq 0}$ be the Rosenblatt process with Hurst index $H \in (1/2, 1)$. We prove joint continuity for the local time of $Z$, and establish Hölder conditions for the local time. These results are then used to study the irregularity of the sample paths of $Z$. Based on analogy with similar known results in the case of fractional Brownian motion, we believe our results are sharp. A main ingredient of our proof is a rather delicate spectral analysis of arbitrary linear combinations of integral operators, which arise from the representation of the Rosenblatt process as an element in the second chaos.
