How Does Tempering Affect the Local and Global Properties of Fractional Brownian Motion?

Ehsan Azmoodeh (), Yuliya Mishura () and Farzad Sabzikar ()
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Ehsan Azmoodeh: University of Liverpool
Yuliya Mishura: Taras Shevchenko National University of Kyiv
Farzad Sabzikar: Iowa State University

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 484-527

Abstract: Abstract The present paper investigates the effects of tempering the power law kernel of the moving average representation of a fractional Brownian motion (fBm) on some local and global properties of this Gaussian stochastic process. Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) are the processes that are considered in order to investigate the role of tempering. Tempering does not change the local properties of fBm including the sample paths and p-variation, but it has a strong impact on the Breuer–Major theorem, asymptotic behavior of the third and fourth cumulants of fBm and the optimal fourth moment theorem.

Keywords: Fractional Brownian motion; Tempered fractional processes; Semi-long memory; Breuer–Major theorem; Limit theorems; Malliavin calculus; 60F17; 60H07; 60G22; 60G15 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-020-01068-z

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