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Related Experiment Videos

Random series and discrete path integral methods: The Lévy-Ciesielski implementation.

Cristian Predescu1, J D Doll

  • 1Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA. Cristian_Predescu@brown.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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This study connects discrete and random series path integral methods for numerical analysis. Both approaches achieve similar convergence rates, O(1/n^2), for the Feynman-Kaç formula.

Area of Science:

  • Numerical analysis
  • Computational mathematics
  • Stochastic processes

Background:

  • Path integral methods are crucial for solving the Feynman-Kaç formula.
  • Discrete and series representations are primary numerical techniques.
  • Understanding their relationship is key for computational efficiency.

Purpose of the Study:

  • To analyze the relationship between discrete and series path integral methods.
  • To interpret discrete methods via Feynman-Kaç formula discretization.
  • To connect Lévy-Ciesielski representation methods to discrete path integrals.

Main Methods:

  • Direct discretization of the Feynman-Kaç formula.
  • Analysis of Lévy-Ciesielski representation (primitive, partial averaging, reweighted).

Related Experiment Videos

  • Establishing connections between series subsequences and discrete path integrals.

    • Main Results:

    • A direct connection is established between discrete and random series path integral methods.
    • Subsequences of Lévy-Ciesielski methods are shown to be discrete path integrals.
    • Sharp estimates for convergence rates of series methods are derived.

    Conclusions:

    • The study bridges discrete and random series path integral approaches.
    • Both methods demonstrate comparable convergence rates, O(1/n^2).
    • This provides a unified understanding for numerical applications of the Feynman-Kaç formula.