Brownian motion
E1601
Markov process
continuous-path process
continuous-time process
physical phenomenon
random process
stochastic process
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)
Statements (53)
| Predicate | Object |
|---|---|
| instanceOf |
Markov process
ⓘ
continuous-path process ⓘ continuous-time process ⓘ physical phenomenon ⓘ random process ⓘ stochastic process ⓘ |
| alsoKnownAs |
Brownian motion
ⓘ
surface form:
Wiener process
|
| 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 |
Langevin dynamics
ⓘ
surface form:
Ornstein–Uhlenbeck process
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 |
Feynman–Kac formula
ⓘ
surface form:
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 ⓘ |
Referenced by (49)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Wiener process
this entity surface form:
Wiener process
this entity surface form:
theory of Brownian motion
subject surface form:
Martingale representation theorem
subject surface form:
Martingale representation theorem
this entity surface form:
Brownian motion is a fundamental martingale for its natural filtration
subject surface form:
Martingale representation theorem
subject surface form:
Itô process
subject surface form:
Itô process
this entity surface form:
Wiener process
subject surface form:
Itô process
this entity surface form:
Wiener process
subject surface form:
Norbert Wiener
this entity surface form:
Wiener process
this entity surface form:
Wiener process
subject surface form:
Ornstein–Uhlenbeck process
subject surface form:
Ornstein–Uhlenbeck process
this entity surface form:
Wiener process
this entity surface form:
Wiener process
this entity surface form:
Brownian motion has stationary increments relative to it
this entity surface form:
Wiener process
this entity surface form:
Wiener process
subject surface form:
Robert Brown (botanist)