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Sampling rare trajectories using stochastic bridges.

Javier Aguilar1, Joseph W Baron1, Tobias Galla1

  • 1Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain.

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We developed a novel sampling method for rare events in stochastic processes using stochastic bridges. This technique accurately preserves rare trajectory statistics and offers insights into noise approximations.

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Area of Science:

  • Computational Physics
  • Stochastic Processes
  • Statistical Mechanics

Background:

  • Quantifying rare events in stochastic processes presents significant computational challenges.
  • Existing methods may struggle with accurately capturing the statistics of infrequent occurrences.

Purpose of the Study:

  • To introduce an efficient sampling method for rare events in stochastic processes.
  • To preserve the statistical properties of rare trajectories accurately.
  • To compare the method with established approximations like Wentzel-Kramers-Brillouin (WKB).

Main Methods:

  • Construction of an ensemble of stochastic trajectories constrained between fixed start and end points (stochastic bridges).
  • Assigning statistical weights to bridges to focus on rare events.
  • Comparison of generated stochastic bridges with WKB optimal paths.

Main Results:

  • The method successfully focuses computational resources on rare events while preserving their statistics.
  • Generated stochastic bridges converge to WKB optimal paths in the low-noise limit.
  • The approach provides a means to evaluate WKB approximation accuracy at finite noise levels.

Conclusions:

  • The stochastic bridge sampling method offers an effective solution for studying rare events in stochastic processes.
  • This method validates and extends the applicability of WKB approximations.
  • It provides a robust tool for computational analysis in fields relying on stochastic modeling.