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Linear Fractional Stable Motion (LFSM) of Hurst parameter $H$ and ofstability parameter $\al$, is one of the most classical extensions of thewell-known Gaussian Fractional Brownian Motion (FBM), to the setting ofheavy-tailed stable distributions \cite{SamTaq,EmMa}. In order to overcome somelimitations of its areas of application, coming from stationarity of itsincrements as well as constancy over time of its self-similarity exponent,Stoev and Taqqu introduced in \cite{stoev2004stochastic} an extension of LFSM,called Linear Multifractional Stable Motion (LMSM), in which the Hurstparameter becomes a function $H(\cdot)$ depending on the time variable $t$.Similarly to LFSM, the tail heaviness of the marginal distributions of LMSM isdetermined by $\al$; also, under some conditions, its self-similarity isgoverned by $H(\cdot)$ and its path roughness is closely related to$H(\cdot)-1/\al$. Namely, it was shown in \cite{stoev2004stochastic} that$H(t_0)$ is the self-similarity exponent of LMSM at a time $t_0\neq 0$;moreover, very recently, it was established in \cite{hamonier2012lmsm}, thatthe quantities $\min_{t\in I} H(t)-1/\al$, and $H(t_0)-1/\al$, are respectivelythe uniform H\"older exponent of LMSM on a compact interval $I$, and its localH\"older exponent at $t_0$.  The main goal of our article, is to construct, using wavelet coefficients ofLMSM, strongly consistent (i.e. almost surely convergent) statisticalestimators of $\min_{t\in I} H(t)$, $H(t_0)$, and $\al$; our estimationresults, are obtained when $\al\in (1,2)$, and, $H(\cdot)$ is a H\"olderfunction smooth enough, with values in a compact subinterval$[\underline{H},\bar{H}]$ of $(1/\al,1)$.

Linear Multifractional Stable Motion: wavelet estimation of $H(\cdot)$ and $\al$ parameters