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

Chebyshev's Theorem to Interpret Standard Deviation01:15

Chebyshev's Theorem to Interpret Standard Deviation

4.2K
Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
4.2K
Uniform Distribution01:19

Uniform Distribution

5.0K
The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular.
Two essential properties of this distribution are
5.0K
Standard Deviation01:10

Standard Deviation

16.6K
The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more variation.
16.6K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

93
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
93
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

4.1K
The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
4.1K
Standard Deviation of Calculated Results01:14

Standard Deviation of Calculated Results

6.2K
Standard deviation measures the spread of data around the mean value. Many large data sets follow a Gaussian distribution, also known as a normal distribution. This distribution is bell-shaped curved, with the most frequently observed value (mean or central value) in the middle. The farther away from the central value, the greater the deviation from the central value, and the lower the frequency.
A broad Gaussian distribution curve has a wider standard deviation, representing a data set with...
6.2K

You might also read

Related Articles

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

Sort by
Same author

Erratum: Dynamical large deviations of linear diffusions [Phys. Rev. E 107, 054111 (2023)].

Physical review. E·2025
Same author

Dynamical large deviations of linear diffusions.

Physical review. E·2023
Same author

Adaptive power method for estimating large deviations in Markov chains.

Physical review. E·2023
Same author

Noise correction of large deviations with anomalous scaling.

Physical review. E·2022
Same author

Learning nonequilibrium control forces to characterize dynamical phase transitions.

Physical review. E·2022
Same author

Role of current fluctuations in nonreversible samplers.

Physical review. E·2021
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Jul 10, 2025

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

8.7K

Large deviations of the stochastic area for linear diffusions.

Johan du Buisson1, Thamu D P Mnyulwa2, Hugo Touchette2

  • 1Institute of Theoretical Physics, Department of Physics, Stellenbosch University, Stellenbosch 7600, South Africa.

Physical Review. E
|November 18, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a method to calculate the generating function for stochastic area in linear stochastic differential equations (SDEs). This allows for analysis of large deviations and diffusion reversibility.

More Related Videos

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

7.9K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
00:10

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.3K

Related Experiment Videos

Last Updated: Jul 10, 2025

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

8.7K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

7.9K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
00:10

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.3K

Area of Science:

  • Mathematical Physics
  • Stochastic Processes
  • Ergodic Theory

Background:

  • The stochastic area of planar Brownian motion was studied by Lévy.
  • For linear stochastic differential equations (SDEs), only the expected value of the stochastic area is known.

Purpose of the Study:

  • To calculate the generating function of the stochastic area for linear SDEs.
  • To extract large deviation functions and an effective SDE for long-time behavior.
  • To obtain asymptotic mean and variance of the stochastic area.

Main Methods:

  • Calculation of the generating function for stochastic area.
  • Analysis of the generating function to derive large deviation functions.
  • Derivation of asymptotic mean and variance from the generating function.

Main Results:

  • A method to compute the generating function for stochastic area in linear SDEs.
  • Identification of large deviation functions and an effective SDE for the long-time limit.
  • Calculation of asymptotic mean and variance, crucial for diffusion reversibility analysis.

Conclusions:

  • The study provides a comprehensive framework for analyzing the stochastic area in linear SDEs.
  • Results offer insights into the long-time behavior and reversibility of diffusion processes.
  • The developed methods can be applied to study both reversible and irreversible linear SDEs.