Large-deviation probabilities for correlated Gaussian processes and intermittent dynamical systems

Area of Science:

• Statistical Mechanics
• Time Series Analysis
• Probability Theory

Background:

• Classical large deviation theory quantifies outlier probabilities in time-averaged, independent, and identically distributed data.
• Understanding deviations in correlated data is crucial for accurate statistical modeling.

Purpose of the Study:

• Investigate large-deviation probabilities (LDPs) for time averages in Gaussian processes with short- and long-range correlations.
• Examine the impact of intermittency on LDPs using a deterministic map.

Main Methods:

• Analysis of large-deviation probabilities (LDPs) for time averages.
• Studying Gaussian processes with varying correlation structures (short- and long-range).
• Numerical illustration using a deterministic intermittent map.

Main Results:

• Long-range correlations in Gaussian processes result in subexponential decay of LDPs.
• A deterministic intermittent map generates long-range correlated time series.
• Intermittency leads to a power law decay of LDPs, irrespective of correlation time finiteness.

Conclusions:

• Long-range correlations fundamentally alter the decay rate of large deviation probabilities.
• Intermittent dynamics provide a mechanism for power-law decay in LDPs, extending beyond standard statistical assumptions.