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

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.8K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.8K
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

7.3K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
7.3K
Reversible and Irreversible Processes01:14

Reversible and Irreversible Processes

4.8K
The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
4.8K
The de Broglie Wavelength02:32

The de Broglie Wavelength

30.8K
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...
30.8K
Simple Harmonic Motion and Uniform Circular Motion01:42

Simple Harmonic Motion and Uniform Circular Motion

4.8K
While simple harmonic motion and uniform circular motion may be two separate concepts, they correlate and interlink with each other. Simple harmonic motion is an oscillatory motion in a system where the net force can be described by Hooke's law, while uniform circular motion is the motion of an object in a circular path at constant speed.
There is an easy way to produce simple harmonic motion by using uniform circular motion. For instance, consider a ball attached to a uniformly rotating...
4.8K
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

8.8K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
8.8K

You might also read

Related Articles

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

Sort by
Same author

A CTRW-driven subdiffusive fractional Brownian bridge in the reconstruction of missing experimental data.

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

Prevalence of hepatitis B and C markers in blood donors deferred from donating blood due to hepatitis-related risk factors.

Asian journal of transfusion science·2026
Same author

Identification of epithelial, mesenchymal, and platelet-associated circulating tumour cells with translational implications in oral squamous cell carcinoma.

Scientific reports·2026
Same author

Recalibration of the European Kidney Function Consortium eGFR Equation for the Indian Population.

Kidney international reports·2026
Same author

The implicit regularizing effect of stochastic resetting in deep learning analysis of anomalous diffusion.

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

An Energy Autonomous Microneedle Array-Based Sensing System for Continuous Biomarker Monitoring.

Advanced science (Weinheim, Baden-Wurttemberg, Germany)·2026

Related Experiment Video

Updated: Oct 23, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.7K

Geometric Brownian motion under stochastic resetting: A stationary yet nonergodic process.

Viktor Stojkoski1,2, Trifce Sandev2,3,4, Ljupco Kocarev2,5

  • 1Faculty of Economics, Ss. Cyril and Methodius University, 1000 Skopje, Macedonia.

Physical Review. E
|August 20, 2021
PubMed
Summary

Stochastic resetting makes geometric Brownian motion (GBM) stationary but nonergodic. Three regimes emerge based on resetting strength, with an optimal rate minimizing self-averaging time for financial applications.

More Related Videos

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.3K
Quantitative Analysis of Random Migration of Cells Using Time-lapse Video Microscopy
07:27

Quantitative Analysis of Random Migration of Cells Using Time-lapse Video Microscopy

Published on: May 13, 2012

17.0K

Related Experiment Videos

Last Updated: Oct 23, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.7K
Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.3K
Quantitative Analysis of Random Migration of Cells Using Time-lapse Video Microscopy
07:27

Quantitative Analysis of Random Migration of Cells Using Time-lapse Video Microscopy

Published on: May 13, 2012

17.0K

Area of Science:

  • Statistical physics
  • Stochastic processes
  • Financial mathematics

Background:

  • Geometric Brownian motion (GBM) is a canonical model for nonstationary and nonergodic dynamics.
  • Stochastic resetting introduces sudden interruptions, renewing a process's dynamics.

Purpose of the Study:

  • Investigate the impact of stochastic resetting on GBM.
  • Analyze how resetting affects stationarity and ergodicity.
  • Identify different long-time regimes and their characteristics.

Main Methods:

  • Mathematical modeling of stochastic resetting applied to GBM.
  • Analysis of the resulting process's statistical properties.
  • Identification of distinct dynamical regimes based on resetting strength.

Main Results:

  • Resetting renders GBM stationary but preserves nonergodicity.
  • Three distinct long-time regimes observed: quenched, unstable, and stable annealed.
  • The stable annealed regime exhibits self-averaging behavior, mimicking ergodic dynamics.
  • Regimes are separated by a self-averaging time, optimizable via resetting rate.

Conclusions:

  • Stochastic resetting plays a crucial role in manifesting nonergodic behavior in GBM.
  • The identified regimes and self-averaging properties offer insights into financial market dynamics.
  • Optimal resetting rates can be determined for practical applications, such as portfolio management.