Intermittency is an ubiquitous property of fully developed turbulence, for Eulerian and Lagrangian fields, and for velocity, passive and active scalars. Intermittency corresponds to multi-scale high fluctuations, with some underlying long-range correlations. Such property is usually characterized using scaling approaches, verified using experimental or numerical data. However there are only few studies devoted to the generation of continuous stochastic processes having non-stationary multifractal properties, able to mimic Eulerian or Lagrangian velocity or passive scalar time series. Here we review recent works on this topic, and we provide stochastic simulations in order to verify the theoretical predictions. In the lognormal framework we provide a $h-\mu$ plane expressing the scale invariant properties of these simulations.