Regularity of multifractional moving average processes with random Hurst exponent

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:140

Article

Loboda, Dennis¹  Mies, Fabian¹  Steland, Ansgar¹ 

[1] Rhein Westfal TH Aachen, Inst Stat, Wullnerstr 3, D-52062 Aachen, Germany

关键词: Multifractional Brownian motion;    Random Holder exponent;    Matern process;    Local self-similarity;    Random field;   

DOI  :  10.1016/j.spa.2021.05.008

来源: Elsevier

【 摘 要 】

A recently proposed alternative to multifractional Brownian motion (mBm) with random Hurst exponent is studied, which we refer to as Ito-mBm. It is shown that Ito-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 Holder 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 Matern process. (C) 2021 Published by Elsevier B.V.

【 授权许可】

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