论文标题
随机赫斯特指数的多曲线移动平均流程的规律性
Regularity of multifractional moving average processes with random Hurst exponent
论文作者
论文摘要
研究了一种最近提出的具有随机Hurst指数的多曲线布朗运动（MBM）的替代方案，我们称为ITô-MBM。结果表明，Itô-MBM在本地自相似。与MBM相比，其路径规律性几乎不受功能性Hurst参数的粗糙度的影响。路径性特性是通过类似于Kolmogorov-Chentsov定理的新的多项式矩条件建立的，允许随机的局部Hölder指数。我们的结果适用于一系列的移动平均过程，在该过程中，路径规律性和长期内存属性可能被解耦，例如进行Matérn过程的多曲线概括。
A recently proposed alternative to multifractional Brownian motion (mBm) with random Hurst exponent is studied, which we refer to as Itô-mBm. It is shown that Itô-mBm is locally self-similar. In contrast to mBm, its pathwise regularity is almost unaffected by the roughness of the functional Hurst parameter. The pathwise properties are established via a new polynomial moment condition similar to the Kolmogorov-Chentsov theorem, allowing for random local Hölder exponents. Our results are applicable to a broad class of moving average processes where pathwise regularity and long memory properties may be decoupled, e.g. to a multifractional generalization of the Matérn process.
