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.

All labels observed (5)

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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 (49)

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.