Brownian motion

E1601

Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.

AI illustration

How this image was made

AI-generated illustration of Brownian motion

This AI-generated illustration was produced by black-forest-labs/FLUX.2-dev (1024x1024) from a prompt written by openai/gpt-oss-120b from the entity's label + description.

Prompt

Generate an image of Brownian motion (Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.)

All labels observed (5)

How this entity was disambiguated

Statements (53)

Predicate Object
instanceOf Markov process ⓘ
continuous-path process ⓘ
continuous-time process ⓘ
physical phenomenon ⓘ
random process ⓘ
stochastic process ⓘ
alsoKnownAs Wiener process ⓘ
linked to: Brownian motion
cause collisions with molecules of the surrounding medium ⓘ
describedAs jittery movement of microscopic particles ⓘ
random motion of particles suspended in a fluid ⓘ
dimension one-dimensional in its standard form ⓘ
discoveredBy Robert Brown ⓘ
discoveryYear 1827 ⓘ
field biology ⓘ
chemistry ⓘ
materials science ⓘ
mathematical finance ⓘ
probability theory ⓘ
statistical physics ⓘ
stochastic calculus ⓘ
generalization Ornstein–Uhlenbeck process ⓘ
linked to: Langevin dynamics

fractional Brownian motion ⓘ
multi-dimensional Brownian motion ⓘ
hasMean zero ⓘ
hasProperty Gaussian increments ⓘ
continuous sample paths ⓘ
starts at zero with probability 1 ⓘ
stationary independent increments ⓘ
mathematicalFormalizationBy Norbert Wiener ⓘ
mathematicalFormalizationYear 1923 ⓘ
namedAfter Robert Brown ⓘ
observedIn microscopic particles in fluids ⓘ
suspensions of pollen grains in water ⓘ
providedEvidenceFor existence of atoms ⓘ
molecular nature of matter ⓘ
relatedConcept Fokker–Planck equation ⓘ
Langevin dynamics ⓘ
central limit theorem ⓘ
diffusion ⓘ
random walk ⓘ
samplePathProperty almost surely nowhere differentiable ⓘ
theoreticalExplanationBy Albert Einstein ⓘ
Marian Smoluchowski ⓘ
theoreticalExplanationYear 1905 ⓘ
usedIn Black–Scholes option pricing model ⓘ
Einstein–Smoluchowski relation ⓘ
Langevin equation modeling ⓘ
derivation of the diffusion equation ⓘ
modeling molecular motion in cells ⓘ
modeling particle diffusion ⓘ
modeling polymer dynamics ⓘ
modeling stock price dynamics ⓘ
varianceGrowth proportional to time ⓘ

How these facts were elicited

Referenced by (59)

Full triples — surface form annotated when it differs from this entity's canonical label.

Albert Einstein → knownFor → Brownian motion ⓘ
Brownian motion → alsoKnownAs → Wiener process ⓘ
linked to: Brownian motion
Fokker–Planck equation → describes → Brownian motion ⓘ
Marian Smoluchowski → fieldOfWork → Brownian motion ⓘ
Jean Perrin → studied → Brownian motion ⓘ
Itô calculus → coreObject → Brownian motion ⓘ
Itô calculus → appliesTo → Brownian motion ⓘ
Girsanov theorem → appliesTo → Brownian motion ⓘ
Robert Brown → knownFor → Brownian motion ⓘ
Robert Brown → discovered → Brownian motion ⓘ
Robert Brown → hasConceptNamedAfter → Brownian motion ⓘ
Norbert Wiener → knownFor → Wiener process ⓘ
linked to: Brownian motion
soft matter physics → usesConcept → Brownian motion ⓘ
Paul Langevin → knownFor → theory of Brownian motion ⓘ
linked to: Brownian motion
Ornstein–Uhlenbeck process → relatedTo → Brownian motion ⓘ
Martingale representation theorem → dealsWith → Brownian motion ⓘ
Martingale representation theorem → conclusion → Brownian motion is a fundamental martingale for its natural filtration ⓘ
linked to: Brownian motion
Martingale representation theorem → representationWithRespectTo → Brownian motion ⓘ
Itô process → hasDrivingProcess → Brownian motion ⓘ
subject linked to: Itô processes
Itô process → hasDrivingProcess → Wiener process ⓘ
subject linked to: Itô processes
linked to: Brownian motion
Itô process → specialCase → Brownian motion ⓘ
subject linked to: Itô processes
Heart of Gold → associatedWith → Brownian motion ⓘ
Random Walk and the Theory of Brownian Motion → usesConcept → Wiener process ⓘ
linked to: Brownian motion
Laplace operator → relatedProcess → Brownian motion ⓘ
Norbert Wiener → knownFor → Wiener process ⓘ
subject linked to: Wiener
linked to: Brownian motion
Wiener → hasNotableBearer → Wiener process ⓘ
linked to: Brownian motion
Ornstein–Uhlenbeck process → drivenBy → Brownian motion ⓘ
subject linked to: OU process
Ornstein–Uhlenbeck process → hasDrivingNoise → Wiener process ⓘ
subject linked to: OU process
linked to: Brownian motion
Clark–Ocone formula → uses → Brownian motion ⓘ
Brownian filtration → associatedWith → Brownian motion ⓘ
Brownian filtration → associatedWith → Wiener process ⓘ
linked to: Brownian motion
Brownian filtration → hasProperty → Brownian motion has stationary increments relative to it ⓘ
linked to: Brownian motion
Gaussian process → hasSpecialCase → Brownian motion ⓘ
Gaussian process → hasSpecialCase → Wiener process ⓘ
linked to: Brownian motion
Wiener measure → associatedWith → Wiener process ⓘ
linked to: Brownian motion
Wiener measure → hasCoordinateProcess → Brownian motion ⓘ
Stratonovich integral → typicalIntegrator → Brownian motion ⓘ
Itô integral → basedOn → Brownian motion ⓘ
Itô isometry → appliesTo → Brownian motion ⓘ
Pithoprakta → inspiredBy → Brownian motion ⓘ
Robert Brown (botanist) → discovered → Brownian motion ⓘ
subject linked to: R.Br.
Robert Brown (botanist) → notableConcept → Brownian motion ⓘ
subject linked to: R.Br.