Poisson Processes

URI: https://gptkb.org/entity/Poisson_Processes

GPTKB entity

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Statements (50)

Predicate	Object
gptkbp:instanceOf	gptkb:stochastic_process
gptkbp:application	modeling arrivals in queues modeling insurance claims modeling network packet arrivals modeling phone call arrivals modeling radioactive decay modeling random events in time
gptkbp:characteristic	exp(lambda t (e^{iu}-1))
gptkbp:distributionOfIncrements	gptkb:Poisson_distribution
gptkbp:firstDescribed	1907
gptkbp:generalizes	gptkb:Bernoulli_process
gptkbp:hasGenerator	difference operator
gptkbp:hasInfinitesimalGenerator	lambda (f(n+1)-f(n))
gptkbp:hasInterarrivalTimeDistribution	gptkb:exponential_distribution
gptkbp:hasKolmogorovBackwardEquation	dP/dt = lambda(P(n+1)-P(n))
gptkbp:hasKolmogorovForwardEquation	dP/dt = lambda(P(n-1)-P(n))
gptkbp:hasLaplaceTransform	exp(lambda t (s-1))
gptkbp:hasLimitingDistribution	gptkb:Poisson_distribution
gptkbp:hasMathematicalExpectation	lambda * t
gptkbp:hasProperty	gptkb:Markov_property independent increments stationary increments
gptkbp:hasSamplePaths	piecewise constant right-continuous
gptkbp:hasSpecialCase	gptkb:stochastic_process
gptkbp:hasStateSpace	non-negative integers
gptkbp:hasTransitionProbability	Poisson probability formula
gptkbp:hasType	gptkb:compound_Poisson_process homogeneous Poisson process non-homogeneous Poisson process
gptkbp:hasVariance	lambda * t
https://www.w3.org/2000/01/rdf-schema#label	Poisson Processes
gptkbp:isContinuousTime	true
gptkbp:isDiscreteState	true
gptkbp:isMemoryless	true
gptkbp:namedAfter	gptkb:Siméon_Denis_Poisson
gptkbp:parameter	rate (lambda)
gptkbp:relatedTo	gptkb:exponential_distribution Markov chain birth process jump process renewal process
gptkbp:usedIn	gptkb:probability_theory finance physics queueing theory statistics telecommunications
gptkbp:bfsParent	gptkb:John_Kingman
gptkbp:bfsLayer	4