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Maps for distributions and their time evolution.

E Forest1, D S Robin

  • 1High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study introduces a new method for analyzing dynamical stochastic processes by using deterministic trajectories as basis functions. This approach simplifies mapping stochastic processes and has potential applications in fields like electron storage rings.

Area of Science:

  • Physics
  • Applied Mathematics

Background:

  • Many complex systems involve dynamical stochastic processes superimposed on deterministic foundations.
  • Understanding these combined dynamics is crucial for analyzing real-world phenomena.

Purpose of the Study:

  • To present a novel method for analyzing dynamical stochastic processes.
  • To utilize deterministic trajectories as basis functions for stochastic distributions.

Main Methods:

  • The proposed method employs the trajectory of a deterministic process as basis functions.
  • This allows for the computation of a map for the superimposed stochastic process.

Main Results:

  • A method is presented to compute a map for stochastic processes using deterministic trajectories.

Related Experiment Videos

  • The technique is demonstrated for elementary applications.

    • Conclusions:

    • The developed method offers a new way to analyze systems with both deterministic and stochastic components.
    • Potential applications exist in areas like electron storage rings and other devices affected by small stochasticity.