Estimation of drift and diffusion functions from unevenly sampled time-series data.

Area of Science:

• Complex systems analysis
• Stochastic process modeling

Background:

• Physical systems are often modeled as stochastic processes.
• Irregularly spaced time-series data pose challenges for model estimation.

Purpose of the Study:

• To extend existing methods for estimating drift and diffusion functions from irregularly sampled time-series data.
• To provide flexible tools applicable to diverse stochastic systems, including those with non-Markovian dynamics or measurement noise.

Main Methods:

• Developed extensions of two established methods for time-series analysis.
• Applied these methods to estimate drift and diffusion coefficients from irregularly sampled data.

Main Results:

• Demonstrated the flexibility and applicability of the extended methods.
• Successfully analyzed a paleoclimatological isotope record with irregular sampling.

Conclusions:

• The presented methods enhance the analysis of stochastic systems with challenging data.
• Provides a framework for gaining insights into physical processes from real-world, noisy, and irregularly sampled observations.