Regularity of Multifractional Moving Average Processes with Random Hurst Exponent

Journal article

Dennis Loboda, Fabian Mies, Ansgar Steland
Stochastic Processes and their Applications, vol. 140, 2021, pp. 21-48

DOI: 10.1016/j.spa.2021.05.008

arXiv Video

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APA Click to copy
Loboda, D., Mies, F., & Steland, A. (2021). Regularity of Multifractional Moving Average Processes with Random Hurst Exponent. Stochastic Processes and Their Applications, 140, 21–48. https://doi.org/10.1016/j.spa.2021.05.008

Chicago/Turabian Click to copy
Loboda, Dennis, Fabian Mies, and Ansgar Steland. “Regularity of Multifractional Moving Average Processes with Random Hurst Exponent.” Stochastic Processes and their Applications 140 (2021): 21–48.

MLA Click to copy
Loboda, Dennis, et al. “Regularity of Multifractional Moving Average Processes with Random Hurst Exponent.” Stochastic Processes and Their Applications, vol. 140, 2021, pp. 21–48, doi:10.1016/j.spa.2021.05.008.

BibTeX Click to copy

@article{loboda2021a,
  title = {Regularity of Multifractional Moving Average Processes with Random Hurst Exponent},
  year = {2021},
  journal = {Stochastic Processes and their Applications},
  pages = {21-48},
  volume = {140},
  doi = {10.1016/j.spa.2021.05.008},
  author = {Loboda, Dennis and Mies, Fabian and Steland, Ansgar}
}

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.

Keywords: multifractional Brownian motion; random Hölder exponent; Matérn process; local self-similarity; random field