Fokker–Planck equation

E8633
evolution equation partial differential equation stochastic process equation

The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.

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Observed surface forms (4)

Surface form Occurrences
Kolmogorov forward equation 3
Smoluchowski diffusion equation 2
Ornstein–Uhlenbeck process 1

Statements (47)

Predicate Object
instanceOf evolution equation ⓘ
partial differential equation ⓘ
stochastic process equation ⓘ
alsoKnownAs Fokker–Planck equation ⓘ
surface form: forward Kolmogorov equation
appliesTo Markovian dynamics ⓘ
systems with Gaussian noise ⓘ
assumes Markov property ⓘ
canBeDerivedFrom Langevin dynamics ⓘ
canBeWrittenIn conservation form ⓘ
describes Brownian motion ⓘ
time evolution of probability density functions ⓘ
time evolution of stochastic processes ⓘ
expresses conservation of probability ⓘ
field applied mathematics ⓘ
mathematical physics ⓘ
probability theory ⓘ
generalizes classical diffusion equation ⓘ
governs probability density function ⓘ
hasSolutionType probability density function over state space ⓘ
hasTerm diffusion term ⓘ
drift term ⓘ
models Markov processes ⓘ
continuous-time stochastic processes ⓘ
diffusion with drift ⓘ
namedAfter Adriaan Fokker ⓘ
Max Planck ⓘ
relatedTo Kolmogorov backward equation ⓘ
Langevin dynamics ⓘ
surface form: Langevin equation

Ornstein–Uhlenbeck process ⓘ
diffusion equation ⓘ
master equation ⓘ
timeDependent yes ⓘ
type second-order partial differential equation ⓘ
usedFor escape rate calculations ⓘ
first-passage time problems ⓘ
noise-induced transitions ⓘ
non-equilibrium statistical mechanics ⓘ
transport phenomena ⓘ
usedIn chemical physics ⓘ
diffusion theory ⓘ
financial mathematics ⓘ
neuroscience ⓘ
plasma physics ⓘ
population dynamics ⓘ
quantum optics ⓘ
statistical physics ⓘ
stochastic processes ⓘ

Referenced by (16)

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

Fokker–Planck equation → alsoKnownAs → Fokker–Planck equation ⓘ
this entity surface form: forward Kolmogorov equation
Kolmogorov backward equation → complements → Fokker–Planck equation ⓘ
Kolmogorov backward equation → complements → Fokker–Planck equation ⓘ
this entity surface form: Kolmogorov forward equation
Adriaan Fokker → hasEponym → Fokker–Planck equation ⓘ
Adriaan Fokker → hasNameInFormula → Fokker–Planck equation ⓘ
fluctuation–dissipation theorem → isRelatedTo → Fokker–Planck equation ⓘ
Adriaan Fokker → knownFor → Fokker–Planck equation ⓘ
Marian Smoluchowski → knownFor → Fokker–Planck equation ⓘ
this entity surface form: Smoluchowski diffusion equation
Adriaan Fokker → notableConcept → Fokker–Planck equation ⓘ
Brownian motion → relatedConcept → Fokker–Planck equation ⓘ
Einstein–Smoluchowski relation → relatedConcept → Fokker–Planck equation ⓘ
Feynman–Kac formula → relatedTo → Fokker–Planck equation ⓘ
this entity surface form: Kolmogorov forward equation
Langevin dynamics → relatedTo → Fokker–Planck equation ⓘ
Langevin dynamics → relatedTo → Fokker–Planck equation ⓘ
this entity surface form: Ornstein–Uhlenbeck process
Markov processes → relatedTo → Fokker–Planck equation ⓘ
subject surface form: Markov process
this entity surface form: Kolmogorov forward equation
Smoluchowski coagulation equation → relatedTo → Fokker–Planck equation ⓘ
this entity surface form: Smoluchowski diffusion equation