Tempered fractional multistable motion and tempered multifractional stable motion

¹ Center for Applied Mathematics, Tianjin University, Tianjin, China.
² Regularity Team, Inria, France.

^* Corresponding author: fanxiequan@hotmail.com

Received: 29 December 2016
Accepted: 11 July 2018

Abstract

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.