Tempered fractional Brownian and stable motions of second kind

Farzad Sabzikar and Donatas Surgailis

Statistics & Probability Letters, 2018, vol. 132, issue C, 17-27

Abstract: Meerschaert and Sabzikar (2013, 2016) introduced tempered fractional Brownian/stable motion (TFBM/TFSM) by including an exponential tempering factor in the moving average representation of FBM/FSM. The present paper discusses another tempered version of FBM/FSM, termed tempered fractional Brownian/stable motion of second kind (TFBM II/TFSM II). We prove that TFBM/TFSM and TFBM II/TFSM II are different processes. Particularly, large time properties of TFBM II/TFSM II are similar to those of FBM/FSM and are in deep contrast to large time properties of TFBM/TFSM.

Keywords: Tempered fractional Brownian/stable motion; Tempered fractional Brownian/stable noise; Tempered fractional integration; Local and global self-similarity (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (8)

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DOI: 10.1016/j.spl.2017.08.015

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