  We investigate the properties of multifractal products of geometric Gaussian
processes with possible long-range dependence and geometric Ornstein-Uhlenbeck
processes driven by L\'{e}vy motion and their finite and infinite
superpositions. We present the general conditions for the $L_q$ convergence of
cumulative processes to the limiting processes and investigate their $q$-th
order moments and R\'{e}nyi functions, which are nonlinear, hence displaying
the multifractality of the processes as constructed. We also establish the
corresponding scenarios for the limiting processes, such as log-normal,
log-gamma, log-tempered stable or log-normal tempered stable scenarios.
