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



Azmoodeh, Ehsan ORCID: 0000-0002-0401-793X, Mishura, Yuliya and Sabzikar, Farzad
(2022) How Does Tempering Affect the Local and Global Properties of Fractional Brownian Motion? JOURNAL OF THEORETICAL PROBABILITY, 35 (1). pp. 484-527.

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Abstract

The present paper investigates the effects of tempering the power law kernel of 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 3rd and 4th cumulants of fBm and the optimal fourth moment theorem.

Item Type: Article
Uncontrolled Keywords: Fractional Brownian motion, Tempered fractional processes, Semi-long memory, Breuer-Major theorem, Limit theorems, Malliavin calculus
Depositing User: Symplectic Admin
Date Deposited: 02 Jun 2020 09:49
Last Modified: 18 Jan 2023 23:50
DOI: 10.1007/s10959-020-01068-z
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3089307