This work defines two classes of processes, that we term tempered fractional multistable motion and tempered multifractional stable motion. They are extensions of fractional multistable motion and multifractional stable motion, respectively, obtained by adding an exponential tempering to the integrands. We investigate certain basic features of these processes, including scaling property, tail probabilities, absolute moment, sample path properties, pointwise Hölder exponent, Hölder continuity of quasi norm, (strong) localisability and semi-long-range dependence structure. These processes may provide useful models for data that exhibit both dependence and varying local regularity/intensity of jumps.
Accepté le :
DOI : 10.1051/ps/2018012
Mots-clés : Stable processes, multistable processes, multifractional processes, sample paths, long-range dependence, localisability
@article{PS_2019__23__37_0,
author = {Fan, Xiequan and L\'evy V\'ehel, Jacques},
title = {Tempered fractional multistable motion and tempered multifractional stable motion},
journal = {ESAIM: Probability and Statistics},
pages = {37--67},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2018012},
mrnumber = {3921881},
zbl = {1411.60072},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2018012/}
}
TY - JOUR AU - Fan, Xiequan AU - Lévy Véhel, Jacques TI - Tempered fractional multistable motion and tempered multifractional stable motion JO - ESAIM: Probability and Statistics PY - 2019 SP - 37 EP - 67 VL - 23 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2018012/ DO - 10.1051/ps/2018012 LA - en ID - PS_2019__23__37_0 ER -
%0 Journal Article %A Fan, Xiequan %A Lévy Véhel, Jacques %T Tempered fractional multistable motion and tempered multifractional stable motion %J ESAIM: Probability and Statistics %D 2019 %P 37-67 %V 23 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2018012/ %R 10.1051/ps/2018012 %G en %F PS_2019__23__37_0
Fan, Xiequan; Lévy Véhel, Jacques. Tempered fractional multistable motion and tempered multifractional stable motion. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 37-67. doi : 10.1051/ps/2018012. http://archive.numdam.org/articles/10.1051/ps/2018012/
[1] , and , The asymptotic depedence structure of the linear frational Lévy motion. Lith. Math. J. 31 (1991) 1–19. | DOI | MR | Zbl
[2] and , Linear multifractional stable motion: fine path properties. Rev. Mat. Iberoam. 30 (2014) 1301–1354. | DOI | MR | Zbl
[3] , Tangent fields and the local structure of random fields. J. Theor. Probab. 15 (2002) 731–750. | DOI | MR | Zbl
[4] , The local structure of random processes. J. Lond. Math. Soc. 67 (2003) 657–672. | DOI | MR | Zbl
[5] and Multifractional, multistable, and other processes with prescribed local form. J. Theor. Probab. 22 (2009) 375–401. | DOI | MR | Zbl
[6] and , Multistable Processes and Localisability. Stoch. Models 28 (2012) 503–526. | DOI | MR | Zbl
[7] , and Localizable moving average symmetric stable and multistable processes. Stoch. Models 25 (2009) 648–672. | DOI | MR | Zbl
[8] and Incremental moments and Hölder exponents of multifractional multistable processes. ESAIM: PS 17 (2013) 135–178. | DOI | Numdam | MR | Zbl
[9] and , Tempered fractional stable motion. J. Theoret. Probab. 29 (2016) 681–706. | DOI | MR | Zbl
[10] , Bibliography on stable distributions, processes and related topics. Available at: http://academic2.american.edu/jpnolan/stable/StableBibliography.pdf (2010).
[11] and , Stable Non-Gaussian Random Processes. Chapman and Hall, London (1994). | MR | Zbl
[12] and , Stochastic properties of the linear multifractional stable motion. Adv. Appl. Probab. 36 (2004) 1085–1115. | DOI | MR | Zbl
[13] and , Path properties of the linear multifractional stable motion. Fractals 13 (2005) 157–178. | DOI | MR | Zbl
[14] , , , , and , Towards synthesis of solar wind and geomagnetic scaling exponents: a fractional Lévy motion model. Space Sci. Rev. 121 (2005) 271–284. | DOI
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