  The main goal of this paper is to construct a wavelet-type random series
representation for a random field $X$, defined by a multistable stochastic
integral, which generates a multifractional multistable Riemann-Liouville
(mmRL) process $Y$. Such a representation provides, among other things, an
efficient method of simulation of paths of $Y$. In order to obtain it, we
expand in the Haar basis the integrand associated with $X$ and we use some
fundamental properties of multistable stochastic integrals. Then, thanks to the
Abel's summation rule and the Doob's maximal inequality for discrete
submartingales, we show that this wavelet-type random series representation of
$X$ is convergent in a strong sense: almost surely in some spaces of continuous
functions. Also, we determine an estimate of its almost sure rate of
convergence in these spaces.

Probability