Numerical simulation of quasi-multifractal diffusion process

摘要

The properties of quasi-multifractal diffusion process are discussed. A discrete model of the process is constructed, and a method is proposed for calculating the quasi-multifractal spectrum, based on statistical processing of its realizations. An analysis of multifractal properties performed by numerical simulation of the quasi-multifractal spectrum is qualitatively substantiated by examining realizations of the simulated process. The results of numerical simulations suggest that there are three distinct scaling regions. Special attention is given to comparative analyses between numerical and analytical results and between realizations of the proposed process and the well-known multifractal random walk.