Brownian motion (in continuous limit)

URI: https://gptkb.org/entity/Brownian_motion_(in_continuous_limit)

GPTKB entity

Statements (50)

Predicate	Object
gptkbp:instanceOf	gptkb:stochastic_process
gptkbp:alsoKnownAs	gptkb:Wiener_process
gptkbp:dimensions	can be defined in any dimension
gptkbp:distribution	gptkb:normal_distribution
gptkbp:hasCovariance	min(s,t) for times s, t
gptkbp:hasGenerator	Laplacian operator
gptkbp:hasModel	random movement of particles stock prices (in Black-Scholes model)
gptkbp:hasProperty	independent increments stationary increments nowhere differentiable continuous paths
gptkbp:hasScalingProperty	B(at) = sqrt(a) B(t)
gptkbp:hasSpecialCase	gptkb:stochastic_process
gptkbp:hasTransitionDensity	Gaussian kernel
https://www.w3.org/2000/01/rdf-schema#label	Brownian motion (in continuous limit)
gptkbp:introduced	gptkb:Norbert_Wiener
gptkbp:isGaussianProcess	true
gptkbp:isMartingale	true
gptkbp:legalSystem	gptkb:Wiener_measure
gptkbp:limitation	random walk (as step size goes to zero)
gptkbp:meaning	0
gptkbp:origin	mathematical model of physical Brownian motion
gptkbp:samplePath	almost surely continuous almost surely nowhere differentiable
gptkbp:satisfies	gptkb:Markov_property
gptkbp:solvedBy	gptkb:stochastic_process
gptkbp:startDate	0
gptkbp:usedIn	gptkb:heat_equation gptkb:percolation_theory gptkb:probability_theory gptkb:signal_processing gptkb:statistical_mechanics gptkb:stochastic_process ecology hydrodynamics mathematical biology mathematical finance option pricing physics quantum mechanics potential theory random matrix theory polymer science Ito calculus random fractals Feynman-Kac formula
gptkbp:variant	t (time parameter)
gptkbp:bfsParent	gptkb:Drunkard's_Walk
gptkbp:bfsLayer	6