Bounded lognormal cascades as quasi-multiaffine random processes

A new model for simulating non-negative random processes is developed. The model is based on a bounded random multiplicative cascade with a lognormal generator with the scale parameter dependent on the number of steps in the cascade. It is shown, both analytically and numerically, that the simulated field has multiaffine properties within some restricted range of scales. This type of random processes is defined here as quasi-multiaffine. A procedure for retrieving the modeling parameters from real data is also discussed.