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Related Experiment Video

Updated: May 18, 2026

Optical Trap Loading of Dielectric Microparticles In Air
08:57

Optical Trap Loading of Dielectric Microparticles In Air

Published on: February 5, 2017

Extended Kramers-Moyal analysis applied to optical trapping.

Christoph Honisch1, Rudolf Friedrich, Florian Hörner

  • 1Institute for Theoretical Physics, University of Muenster, D-48149 Muenster, Germany. c.honisch@uni-muenster.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

Finite time effects in Kramers-Moyal analysis can cause errors. This study extends a method to estimate these effects more reliably using Monte Carlo error propagation, improving analysis of complex systems.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Kramers-Moyal analysis is crucial for studying complex systems via stochastic time series.
  • Insufficient sampling intervals lead to systematic errors, known as finite time effects.
  • Existing methods for estimating Kramers-Moyal coefficients are limited by these finite time effects.

Purpose of the Study:

  • To provide new insights into finite time effects in Kramers-Moyal analysis.
  • To discuss limitations of prior methods for estimating coefficients under these effects.
  • To enhance the reliability of Kramers-Moyal coefficient estimation.

Main Methods:

  • Extended a previously published method for estimating Kramers-Moyal coefficients.
  • Incorporated Monte Carlo error propagation to compute error estimates for parameters.

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Last Updated: May 18, 2026

Optical Trap Loading of Dielectric Microparticles In Air
08:57

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Published on: February 5, 2017

Construction of a High Resolution Microscope with Conventional and Holographic Optical Trapping Capabilities
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Construction of a High Resolution Microscope with Conventional and Holographic Optical Trapping Capabilities

Published on: April 22, 2013

Direct Force Measurements of Subcellular Mechanics in Confinement using Optical Tweezers
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  • Applied the extended method to experimental data from an optical trapping experiment.

    • Main Results:

    • Identified and quantified finite time effects impacting Kramers-Moyal analysis.
    • Demonstrated improved reliability in estimating Kramers-Moyal coefficients.
    • Observed an increased Markov-Einstein time scale due to particle-fluid interactions.

    Conclusions:

    • The extended method provides more reliable Kramers-Moyal coefficient estimations, mitigating finite time effects.
    • Memory effects from particle-fluid interactions influence the observed time scales.
    • The classical overdamped Markov model accurately describes Brownian motion above the Markov-Einstein time scale.