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Regularity of multifractional moving average processes with random Hurst exponent
Stochastic Processes and their Applications ( IF 1.4 ) Pub Date : 2021-06-08 , DOI: 10.1016/j.spa.2021.05.008
Dennis Loboda , Fabian Mies , Ansgar Steland

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–Centsov 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.



中文翻译:

具有随机 Hurst 指数的多重分形移动平均过程的规律性

研究了最近提出的具有随机 Hurst 指数的多分数布朗运动 (mBm) 的替代方案,我们将其称为 Itô-mBm。结果表明,Itô-mBm 是局部自相似的。与 mBm 相比,其路径规律性几乎不受函数 Hurst 参数粗糙度的影响。路径属性是通过类似于 Kolmogorov-Centsov 定理的新多项式矩条件建立的,允许随机局部 Hölder 指数。我们的结果适用于一大类移动平均过程,其中路径规律性和长记忆特性可以解耦,例如,适用于 Matérn 过程的多分数推广。

更新日期:2021-06-15
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