The goal of this paper is to provide a wavelet series representation for Linear Multifractional Stable Motion (LMSM). Instead of using Daubechies wavelets, which are not given in closed form, we use a Haar wavelet, thus yielding a more explicit expression than that in Ayache and Hamonier (in press).

In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in [A. Ayache, F. Roueff, Y. Xiao, Local and asymptotic properties of linear fractional stable sheets, C.R. Acad. Sci. Paris Ser. I. 344 (6) (2007)...

The generalized multifractional Brownian motion (GMBM) is a continuous Gaussian process that extends the classical fractional Brownian motion (FBM) and multifractional Brownian motion (MBM) (SIAM Rev. 10 (1968) 422; INRIA Res. Rept. 2645 (1995); Rev. Mat. Iberoamericana 13 (1997) 19; Fractals: Theory...

Multistable stochastic integrals on R, have been introduced quite recently in Falconer and Liu (2012); they are defined through their characteristic functions. Roughly speaking, in a neighborhood of an arbitrary point x∈R, such an integral can be viewed as a usual stable stochastic integral,...