某些高斯过程局部时间的分数导数
Fractional derivatives of local times for some Gaussian processes
AI总结：
本文研究了满足强局部非确定性性质的高斯过程的局部时间分数导数，证明了其在时间和空间变量上的Hölder连续性及导数阶数的连续性。
摘要：
在本文中，我们考虑满足一定强局部非确定性性质的d维中心高斯过程的局部时间的分数导数。我们首先给出局部时间由Marchaud导数定义在L^p(p≥1)中存在分数导数的条件，并证明这些导数在时间和空间变量上都是Hölder连续的，并且对导数阶数也是连续的。此外，在某些额外假设下，我们利用复积分的方法证明该条件也是局部时间导数存在的必要条件。
英文摘要：
In this article, we consider fractional derivatives of local time for $d-$dimensional centered Gaussian processes satisfying certain strong local nondeterminism property. We first give a condition for existence of fractional derivatives of the local time defined by Marchaud derivatives in $L^p(p\ge1)$ and show that these derivatives are Hölder continuous with respect to both time and space variables and are also continuous with respect to the order of derivatives. Moreover, under some additional assumptions, we show that this condition is also necessary for existence of derivatives of the local time with the help of contour integration.
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