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- Bessel_process abstract "In mathematics, a Bessel process, named after Friedrich Bessel, is a type of stochastic process. The Bessel process of order n is the real-valued process X given bywhere ||·|| denotes the Euclidean norm in Rn and W is an n-dimensional Wiener process (Brownian motion) started from the origin.The n-dimensional Bessel process is the solution to the stochastic differential equationwhere Z is a 1-dimensional Wiener process (Brownian motion). Note that this SDE makes sense for any real parameter (although the drift term is singular at zero). Since W was assumed to have started from the origin the initial condition is X0 = 0.For n ≥ 2, the n-dimensional Wiener process is transient from its starting point: with probability one, Xt > 0 for all t > 0. It is, however, neighbourhood-recurrent for n = 2, meaning that with probability 1, for any r > 0, there are arbitrarily large t with Xt < r; on the other hand, it is truly transient for n > 2, meaning that Xt ≥ r for all t sufficiently large.A notation for the Bessel process of dimension n' started at zero is BES0(n).0- and 2-dimensional Bessel processes are related to local times of Brownian motion via the Ray-Knight theorems.The law of a Brownian motion near x-extrema is the law of a 3-dimensional Bessel process (theorem of Tanaka).".
- Bessel_process wikiPageID "7646799".
- Bessel_process wikiPageRevisionID "599655056".
- Bessel_process hasPhotoCollection Bessel_process.
- Bessel_process subject Category:Stochastic_processes.
- Bessel_process type Abstraction100002137.
- Bessel_process type Cognition100023271.
- Bessel_process type Concept105835747.
- Bessel_process type Content105809192.
- Bessel_process type Hypothesis105888929.
- Bessel_process type Idea105833840.
- Bessel_process type Model105890249.
- Bessel_process type PsychologicalFeature100023100.
- Bessel_process type StochasticProcess113561896.
- Bessel_process type StochasticProcesses.
- Bessel_process comment "In mathematics, a Bessel process, named after Friedrich Bessel, is a type of stochastic process. The Bessel process of order n is the real-valued process X given bywhere ||·|| denotes the Euclidean norm in Rn and W is an n-dimensional Wiener process (Brownian motion) started from the origin.The n-dimensional Bessel process is the solution to the stochastic differential equationwhere Z is a 1-dimensional Wiener process (Brownian motion).".
- Bessel_process label "Bessel process".
- Bessel_process sameAs m.0267rk1.
- Bessel_process sameAs Q4896405.
- Bessel_process sameAs Q4896405.
- Bessel_process sameAs Bessel_process.
- Bessel_process wasDerivedFrom Bessel_process?oldid=599655056.
- Bessel_process isPrimaryTopicOf Bessel_process.