Generic multifractality in exponentials of long memory processes.

Area of Science:

• Stochastic processes
• Statistical physics
• Time series analysis

Background:

• Long-memory processes exhibit power-law decay in their memory kernel.
• Previous studies on multifractality were often limited to specific cases (phi=0).
• Understanding multifractal properties is crucial for analyzing complex systems.

Purpose of the Study:

• To investigate the robustness of multifractal scaling in continuous stochastic processes.
• To generalize existing findings on multifractality to processes with long memory (phi>0).
• To explore the relationship between process parameters and multifractal characteristics.

Main Methods:

• Construction of continuous stochastic processes as exponentials of long-memory processes.
• Characterization of long memory using a power-law kernel with tail exponent phi+1/2.
• Analysis of multifractal spectra (zeta(q)) and scaling behavior.

Main Results:

• Multifractality is demonstrated to be a robust property across a wide range of dimensionless scales for phi>0.
• The intermittency multifractal coefficient is continuously tunable via parameters phi and sigma2.
• A universal scaling function provides a good collapse for multifractal spectra, enabling prediction of exponents.

Conclusions:

• The study generalizes multifractality to a broader class of stochastic processes.
• The findings reveal a tunable intermittency and a universal scaling behavior.
• The results offer a unified framework for understanding multifractal properties in long-memory processes.