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

Probability Laws01:49

Probability Laws

44.0K
Overview
44.0K
Probability in Statistics01:14

Probability in Statistics

22.4K
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
22.4K
Probability Histograms01:17

Probability Histograms

13.2K
A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
13.2K
Probability Distributions01:32

Probability Distributions

11.9K
 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
11.9K
Binomial Probability Distribution01:15

Binomial Probability Distribution

15.4K
A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
15.4K
Poisson Probability Distribution01:09

Poisson Probability Distribution

11.7K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
11.7K

You might also read

Related Articles

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

Sort by
Same author

Effects of Multiplicative Noise in Bistable Dynamical Systems.

Entropy (Basel, Switzerland)·2025
Same author

Emergent gauge symmetry in active Brownian matter.

Physical review. E·2024
Same author

State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates.

Physical review. E·2020
Same author

Finite temperature effects in quantum systems with competing scalar orders.

Journal of physics. Condensed matter : an Institute of Physics journal·2020
Same author

Quantum corrections for the phase diagram of systems with competing order.

Journal of physics. Condensed matter : an Institute of Physics journal·2018
Same author

Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015
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: Jan 26, 2026

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat
11:18

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Published on: September 12, 2014

15.7K

Conditional probabilities in multiplicative noise processes.

Miguel V Moreno1, Daniel G Barci1, Zochil González Arenas2

  • 1Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013 Rio de Janeiro, RJ, Brazil.

Physical Review. E
|April 20, 2019
PubMed
Summary
This summary is machine-generated.

This study simplifies calculating transition probabilities in stochastic differential equations with multiplicative noise. A novel time reparametrization method transforms complex multiplicative noise into simpler additive noise, enabling analytic solutions.

More Related Videos

Modified Experimental Conditions for Noise-Induced Hearing Loss in Mice and Assessment of Hearing Function and Outer Hair Cell Damage
07:13

Modified Experimental Conditions for Noise-Induced Hearing Loss in Mice and Assessment of Hearing Function and Outer Hair Cell Damage

Published on: February 10, 2023

2.8K
Author Spotlight: A Multi-Depth Porcine Model for Comprehensive Study of Burn Injuries and Healing Processes
02:49

Author Spotlight: A Multi-Depth Porcine Model for Comprehensive Study of Burn Injuries and Healing Processes

Published on: February 23, 2024

2.0K

Related Experiment Videos

Last Updated: Jan 26, 2026

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat
11:18

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Published on: September 12, 2014

15.7K
Modified Experimental Conditions for Noise-Induced Hearing Loss in Mice and Assessment of Hearing Function and Outer Hair Cell Damage
07:13

Modified Experimental Conditions for Noise-Induced Hearing Loss in Mice and Assessment of Hearing Function and Outer Hair Cell Damage

Published on: February 10, 2023

2.8K
Author Spotlight: A Multi-Depth Porcine Model for Comprehensive Study of Burn Injuries and Healing Processes
02:49

Author Spotlight: A Multi-Depth Porcine Model for Comprehensive Study of Burn Injuries and Healing Processes

Published on: February 23, 2024

2.0K

Area of Science:

  • Stochastic processes
  • Quantum mechanics
  • Mathematical physics

Background:

  • Stochastic differential equations (SDEs) with multiplicative noise present significant computational challenges.
  • Path integral methods offer a powerful framework for analyzing SDEs.
  • Understanding transition probabilities is crucial in various scientific domains.

Purpose of the Study:

  • To develop an efficient method for calculating transition probabilities in multiplicative noise SDEs.
  • To establish an equivalence between multiplicative noise SDEs and quantum mechanics problems.
  • To provide an analytic solution for a specific nonlinear system.

Main Methods:

  • Utilizing a path integral approach to analyze SDEs.
  • Establishing an analogy between conditional probability in SDEs and quantum particle propagators.
  • Introducing a time reparametrization technique to convert multiplicative noise to additive noise.

Main Results:

  • Demonstrated the equivalence between conditional probability and the propagator of a quantum particle with variable mass.
  • Showcased that time reparametrization transforms multiplicative noise problems into additive noise problems.
  • Provided an explicit analytic computation of the conditional probability for a harmonic oscillator in a nonlinear multiplicative environment.

Conclusions:

  • The proposed path integral method with time reparametrization offers a robust way to solve multiplicative noise SDEs.
  • The established quantum mechanics analogy provides new insights into stochastic processes.
  • The analytic solution for the harmonic oscillator validates the effectiveness of the developed technique.