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 Video

Updated: Sep 9, 2025

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
10:16

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

12.4K

Detecting subtle deviations in Brownian motion representations driven by a Schauder basis.

Massimiliano Frezza1

  • 1MEMOTEF, Sapienza University of Rome, Roma 00161, Italy.

Chaos (Woodbury, N.Y.)
|September 4, 2025
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.1K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.1K
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

1.6K
A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to...
1.6K
The de Broglie Wavelength02:32

The de Broglie Wavelength

26.3K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
26.3K
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

774
When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
774
Difference from Background: Limit of Detection01:05

Difference from Background: Limit of Detection

7.1K
The limit of detection (LOD) is the smallest amount of analyte that can be distinguished from the background noise. The LOD value corresponds to the concentration at which the analyte signal is three times larger than the standard deviation of the blank signal. Below this value, the analyte signal cannot be differentiated from the background noise. It is calculated by dividing the calibration slope by 3 times the standard deviation of the blank signals.
The LOD indicates the presence or absence...
7.1K

You might also read

Related Articles

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

Sort by
Same author

An information theory approach to stock market liquidity.

Chaos (Woodbury, N.Y.)·2024
Same journal

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exact computation of Lyapunov exponents via system parameters in multi-triangle chaotic maps: Bifurcation analysis and circuit realization.

Chaos (Woodbury, N.Y.)·2026
Same journal

Integrating score-based generative modeling and neural ODEs for accurate representation of multiscale chaotic dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A data-driven tuberculosis model with behavioral changes and saturated treatment: Optimal control and cost-effectiveness study.

Chaos (Woodbury, N.Y.)·2026
Same journal

Breathers, rational solutions, and their exact physical spectra in F = 1 spinor Bose-Einstein condensates.

Chaos (Woodbury, N.Y.)·2026
Same journal

Finite invariant sets with bridging points in logistic IFS.

Chaos (Woodbury, N.Y.)·2026
See all related articles

We generated surrogate Brownian motion using Schauder representations. While non-Gaussian versions mimic some properties, only Gaussian constructions truly replicate Brownian motion's randomness and spectral behavior.

Area of Science:

  • Stochastic Processes
  • Mathematical Finance
  • Time Series Analysis

Background:

  • Brownian motion is fundamental in modeling random phenomena.
  • Distinguishing true Brownian motion from surrogates is crucial for accurate analysis.
  • Schauder representation offers a method for constructing stochastic processes.

Purpose of the Study:

  • To construct and analyze surrogate stochastic processes.
  • To investigate the fidelity of non-Gaussian Schauder-based constructions compared to Brownian motion.
  • To identify subtle deviations from true Brownian motion in generated sample paths.

Main Methods:

  • Utilizing the Schauder representation for stochastic process construction.
  • Employing non-Gaussian distributions (beta, uniform) for Schauder coefficients.

More Related Videos

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Published on: September 8, 2016

10.4K
Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System
09:48

Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System

Published on: June 30, 2018

9.0K

Related Experiment Videos

Last Updated: Sep 9, 2025

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
10:16

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

12.4K
Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Published on: September 8, 2016

10.4K
Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System
09:48

Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System

Published on: June 30, 2018

9.0K
  • Applying entropy-based measures and spectral variance analysis for deeper evaluation.

    • Main Results:

    • Non-Gaussian surrogates preserved properties like quadratic variation and covariance structure.
    • Only Gaussian-based constructions maintained consistent spectral behavior and randomness.
    • Subtle, yet significant, deviations from Brownian motion were observed in non-Gaussian variants.

    Conclusions:

    • The Schauder representation can generate realistic Brownian motion surrogates.
    • Gaussian-based constructions are superior in replicating true Brownian motion characteristics.
    • Advanced analytical techniques are necessary to detect subtle differences in stochastic processes.