Exact numerical simulation of power-law noises

Area of Science:

• Computational Physics
• Statistical Mechanics
• Numerical Methods

Background:

• Stochastic processes simulations often require colored noise generation.
• Existing methods may face limitations with unevenly spaced time steps, common in astronomical data.
• Accurate simulation of colored noise is essential for reliable modeling.

Purpose of the Study:

• To introduce an exact numerical method for simulating power-law noises.
• To demonstrate the method's applicability to more general colored noises.
• To provide an efficient and accurate tool for stochastic process simulations.

Main Methods:

• Developed an exact numerical algorithm for simulating power-law noises.
• Ensured the method's validity for all time steps, including unevenly spaced ones.
• Analyzed computational complexity and dependence on desired Gaussianity.

Main Results:

• The proposed method accurately simulates power-law and general colored noises.
• The algorithm is exact even with unevenly spaced time steps.
• It exhibits well-behaved computational complexity and produces nearly perfect Gaussian noise.

Conclusions:

• The presented numerical method offers an exact and efficient solution for simulating colored noises.
• It is particularly valuable for applications with uneven time sampling, such as in astronomical data analysis.
• The method's efficiency is adaptable based on the required level of noise Gaussianity.