Regularity of multifractional moving average processes with random Hurst exponent

Dennis Loboda, Fabian Mies and Ansgar Steland

Stochastic Processes and their Applications, 2021, vol. 140, issue C, 21-48

Abstract: 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.

Keywords: Multifractional Brownian motion; Random Hölder exponent; Matérn process; Local self-similarity; Random field (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2021.05.008

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