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 Concept Videos

You might also read

Related Articles

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

Sort by
Same author

Arthroscopic primary repair of the anterior cruciate ligament with internal brace ligament augmentation: a viable alternative to reconstruction? A systematic literature review and analysis.

BMC musculoskeletal disorders·2026
Same author

Biomechanical Model of Non-Contact Anterior Cruciate Ligament Injury Concerning Shin Angle and Field Surface Traction Parameters-With a Piezo2 Interpretation.

Sports (Basel, Switzerland)·2025
Same author

Lacunary Series and Strong Approximation.

Entropy (Basel, Switzerland)·2025
Same author

Comparative Effectiveness of Supervised and Home-Based Rehabilitation after Anterior Cruciate Ligament Reconstruction in Competitive Athletes.

Journal of clinical medicine·2024
Same author

Random walks on the circle and Diophantine approximation.

Journal of the London Mathematical Society·2024
Same author

[Testing an innovative approach to smartphone sensor-based technology for verification of effectiveness of home exercise].

Orvosi hetilap·2024

Related Experiment Video

Updated: Jul 1, 2025

An Immunocompetent Murine Model for Laser Interstitial Thermal Therapy of Glioblastoma
09:10

An Immunocompetent Murine Model for Laser Interstitial Thermal Therapy of Glioblastoma

Published on: November 15, 2024

400

Some Optimal Conditions for the ASCLT.

István Berkes1, Siegfried Hörmann2

  • 1A. Rényi Institute of Mathematics, Reáltanoda u. 13-15, Budapest, 1053 Hungary.

Journal of Theoretical Probability
|March 14, 2024
PubMed
Summary

This study investigates the behavior of sums of independent random variables. It establishes conditions for the convergence of these sums to a Wiener process, crucial for statistical analysis and probability theory.

Keywords:
Almost sure central limit theoremSums of independent random variablesWeighted averages

More Related Videos

Treatment of Liver Metastases Using an Internal Target Volume Method for Stereotactic Body Radiotherapy
08:54

Treatment of Liver Metastases Using an Internal Target Volume Method for Stereotactic Body Radiotherapy

Published on: May 8, 2018

14.2K
Learning Modern Laryngeal Surgery in a Dissection Laboratory
07:30

Learning Modern Laryngeal Surgery in a Dissection Laboratory

Published on: March 18, 2020

8.1K

Related Experiment Videos

Last Updated: Jul 1, 2025

An Immunocompetent Murine Model for Laser Interstitial Thermal Therapy of Glioblastoma
09:10

An Immunocompetent Murine Model for Laser Interstitial Thermal Therapy of Glioblastoma

Published on: November 15, 2024

400
Treatment of Liver Metastases Using an Internal Target Volume Method for Stereotactic Body Radiotherapy
08:54

Treatment of Liver Metastases Using an Internal Target Volume Method for Stereotactic Body Radiotherapy

Published on: May 8, 2018

14.2K
Learning Modern Laryngeal Surgery in a Dissection Laboratory
07:30

Learning Modern Laryngeal Surgery in a Dissection Laboratory

Published on: March 18, 2020

8.1K

Area of Science:

  • Probability Theory
  • Stochastic Processes
  • Mathematical Statistics

Background:

  • The study builds upon existing research in the convergence of sums of independent random variables.
  • It addresses the relationship between the Kolmogorov condition and the approximation of partial sums by Wiener processes.

Purpose of the Study:

  • To establish the validity of a specific convergence relation under the Kolmogorov condition.
  • To investigate the necessity of the Kolmogorov condition by examining a related 'O' notation.
  • To derive optimal conditions for the convergence when the Kolmogorov condition is not assumed.

Main Methods:

  • The study employs mathematical analysis and probability theory.
  • It utilizes the Kolmogorov condition to establish convergence properties.
  • The methods involve analyzing the remainder term in the Wiener approximation of partial sums.

Main Results:

  • The paper proves that under the Kolmogorov condition, a specific convergence relation holds for almost everywhere continuous functions.
  • It demonstrates that replacing 'o' with 'O' in the condition generally invalidates the relation.
  • An optimal condition for the convergence is derived in terms of the Wiener approximation remainder term.

Conclusions:

  • The Kolmogorov condition is shown to be sufficient for the established convergence.
  • The strictness of the condition is highlighted by the failure of the 'O' notation.
  • The research provides a precise understanding of the conditions required for approximating partial sums with Wiener processes.