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

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This study introduces new methods to model complex systems using irregularly sampled data, improving the estimation of stochastic processes. These techniques offer insights into physical processes from noisy, time-displaced observations.

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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.