Incremental moments and Hölder exponents of multifractional multistable processes
ESAIM: Probability and Statistics, Volume 17 (2013), pp. 135-178.

Multistable processes, that is, processes which are, at each “time”, tangent to a stable process, but where the index of stability varies along the path, have been recently introduced as models for phenomena where the intensity of jumps is non constant. In this work, we give further results on (multifractional) multistable processes related to their local structure. We show that, under certain conditions, the incremental moments display a scaling behaviour, and that the pointwise Hölder exponent is, as expected, related to the local stability index. We compute the precise value of the almost sure Hölder exponent in the case of the multistable Lévy motion, which turns out to reveal an interesting phenomenon.

DOI: 10.1051/ps/2011151
Classification: 60G17, 60G18, 60G22, 60G52
Keywords: localisable processes, multistable processes, multifractional processes, pointwise Hölder regularity
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     title = {Incremental moments and {H\"older} exponents of multifractional multistable processes},
     journal = {ESAIM: Probability and Statistics},
     pages = {135--178},
     publisher = {EDP-Sciences},
     volume = {17},
     year = {2013},
     doi = {10.1051/ps/2011151},
     mrnumber = {3021313},
     zbl = {1292.60050},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2011151/}
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Le Guével, Ronan; Véhel, Jacques Lévy. Incremental moments and Hölder exponents of multifractional multistable processes. ESAIM: Probability and Statistics, Volume 17 (2013), pp. 135-178. doi : 10.1051/ps/2011151. http://www.numdam.org/articles/10.1051/ps/2011151/

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