Noise-Driven Return Statistics: Scaling and Truncation in Stochastic Storage Processes

Area of Science:

• Complex systems analysis
• Stochastic processes and statistical mechanics
• Non-equilibrium dynamics

Background:

• Understanding system behavior under variable forcing is crucial.
• First return time distributions analyze time spent away from a threshold.
• Existing models often use exponential or power laws, which may be insufficient.

Purpose of the Study:

• To investigate the natural emergence of return time distributions in systems with stochastic forcing.
• To propose truncated power laws as a more accurate model for first return times.
• To identify the underlying mechanisms driving these distributions.

Main Methods:

• Development of a minimal stochastic mass balance model.
• Analytical derivation of boundary-independent scaling and truncation properties.
• Validation through numerical simulations.

Main Results:

• A parsimonious mechanism for truncated power law return times was identified.
• Derived scaling and truncation properties were confirmed by simulations.
• The findings demonstrate the natural occurrence of truncated power laws.

Conclusions:

• Truncated power laws are a more appropriate description for first return times in many stochastic systems.
• The identified mechanism provides a theoretical basis for these distributions.
• The results have broad implications for analyzing diverse systems subjected to variable forcing.