Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Optimal prediction and the Klein-Gordon equation.

O H Hald1

  • 1Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA.

Proceedings of the National Academy of Sciences of the United States of America
|April 29, 1999
PubMed
Summary

Optimal prediction accurately estimates future means for Klein-Gordon equation solutions. This method ensures approximate calculations closely match true averages with high probability.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Optimal prediction and the Mori-Zwanzig representation of irreversible processes.

Proceedings of the National Academy of Sciences of the United States of America·2000
Same author

Structure of the zero-pressure-gradient turbulent boundary layer.

Proceedings of the National Academy of Sciences of the United States of America·1997
See all related articles

Area of Science:

  • Mathematical Physics
  • Applied Mathematics
  • Quantum Field Theory

Background:

  • The Klein-Gordon equation describes relativistic quantum mechanics.
  • Predicting the behavior of solutions is crucial for understanding quantum systems.
  • Approximate methods are often used due to the complexity of exact solutions.

Purpose of the Study:

  • To apply the optimal prediction method to calculate future means of Klein-Gordon equation solutions.
  • To analyze the accuracy of approximate methods in predicting these future means.
  • To establish probabilistic bounds on the error of approximate predictions.

Main Methods:

  • Optimal prediction method.
  • Stochastic calculus and probability theory.
  • Analysis of partial differential equations.

Main Results:

  • The optimal prediction method was successfully applied to the Klein-Gordon equation.
  • A probabilistic framework was established to analyze the accuracy of predictions.
  • It was demonstrated that the difference between exact and approximate future means is small with high probability.

Conclusions:

  • The optimal prediction method provides a reliable way to approximate future means of Klein-Gordon equation solutions.
  • The study validates the use of approximate methods within a rigorous probabilistic framework.
  • This work has implications for numerical simulations and theoretical analyses in quantum field theory.

Related Experiment Videos