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.
Aliases (3)
Statements (53)
| Predicate | Object |
|---|---|
| instanceOf |
Markov process
→
continuous-path process → continuous-time process → physical phenomenon → random process → stochastic process → |
| alsoKnownAs |
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 |
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 |
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
→
|