Volume 24, 2020
|Page(s)||1 - 20|
|Published online||20 January 2020|
Estimation of the multifractional function and the stability index of linear multifractional stable processes
University of Economics, The University of Danang,
71 Ngu Hanh Son street,
Danang, Viet Nam.
* Corresponding author: email@example.com
Accepted: 19 June 2019
In this paper we are interested in multifractional stable processes where the self-similarity index H becomes time-dependent, while the stability index α remains constant. Using β- negative power variations ( − 1∕2 < β < 0), we propose estimators for the value at a fixed time of the multifractional function H which satisfies an η-Hölder condition and for α in two cases: multifractional Brownian motion (α = 2) and linear multifractional stable motion (0 < α < 2). We get the consistency of our estimates for the underlying processes together with the rate of convergence.
Mathematics Subject Classification: 60G18 / 60G15 / 60G52
Key words: Stable processes / multifractional processes / negative power variations / multifractional function
© EDP Sciences, SMAI 2020
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