Title: Estimation of the multifractional function and the stability index of linear multifractional stable processes,
Abstract: In this paper we are interested in multifractional stable processes where the
self-similarity index $H$ is a function of time, in other words $H$ becomes
time changing, and the stability index $\alpha$ is a constant. Using $\beta$-
negative power variations ($-1/2<\beta<0$), we propose estimators for the value
of the multifractional function $H$ at a fixed time $t_0$ and for $\alpha$ for
two cases: multifractional Brownian motion ($\alpha=2$) and linear
multifractional stable motion ($0<\alpha<2$). We get the consistency of our
estimates for the underlying processes with the rate of convergence.