Numerical simulation of the realizations and spectra of a quasi-multifractal diffusion process

A discrete model has been developed for a quasi-multifractal diffusion process and a new method for calculating the quasi-multifractal spectrum has been proposed with the use of the statistical processing of the realizations of the process. This method makes it possible to obtain an almost continuous process spectrum, which is impossible by means of traditional analytical methods. The numerical experiments indicate three significantly different regions of the parameters: regions of “monofractality,” “tempered” multifractality, and “strong” multifractality. The model allows deeper insight into the mechanisms of multifractal phenomena in strong turbulence and in the stochastic behavior of financial markets.