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- Kolmogorov_backward_equations_(diffusion) abstract "The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. Both were published by Andrey Kolmogorov in 1931. Later it was realized that the forward equation was already known to physicists under the name Fokker–Planck equation; the KBE on the other hand was new.Informally, the Kolmogorov forward equation addresses the following problem. We have information about the state x of the system at time t (namely a probability distribution ); we want to know the probability distribution of the state at a later time . The adjective 'forward' refers to the fact that serves as the initial condition and the PDE is integrated forward in time. (In the common case where the initial state is known exactly is a Dirac delta function centered on the known initial state).The Kolmogorov backward equation on the other hand is useful when we are interested at time t in whether at a future time s the system will be in a given subset of states B, sometimes called the target set. The target is described by a given function which is equal to 1 if state x is in the target set at time s, and zero otherwise. In other words, , the indicator function for the set B. We want to know for every state x at time what is the probability of ending up in the target set at time s (sometimes called the hit probability). In this case serves as the final condition of the PDE, which is integrated backward in time, from s to t.".
- Kolmogorov_backward_equations_(diffusion) wikiPageID "6419365".
- Kolmogorov_backward_equations_(diffusion) wikiPageRevisionID "566024320".
- Kolmogorov_backward_equations_(diffusion) hasPhotoCollection Kolmogorov_backward_equations_(diffusion).
- Kolmogorov_backward_equations_(diffusion) subject Category:Parabolic_partial_differential_equations.
- Kolmogorov_backward_equations_(diffusion) subject Category:Stochastic_differential_equations.
- Kolmogorov_backward_equations_(diffusion) type Abstraction100002137.
- Kolmogorov_backward_equations_(diffusion) type Communication100033020.
- Kolmogorov_backward_equations_(diffusion) type DifferentialEquation106670521.
- Kolmogorov_backward_equations_(diffusion) type Equation106669864.
- Kolmogorov_backward_equations_(diffusion) type MathematicalStatement106732169.
- Kolmogorov_backward_equations_(diffusion) type Message106598915.
- Kolmogorov_backward_equations_(diffusion) type ParabolicPartialDifferentialEquations.
- Kolmogorov_backward_equations_(diffusion) type PartialDifferentialEquation106670866.
- Kolmogorov_backward_equations_(diffusion) type Statement106722453.
- Kolmogorov_backward_equations_(diffusion) type StochasticDifferentialEquations.
- Kolmogorov_backward_equations_(diffusion) comment "The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. Both were published by Andrey Kolmogorov in 1931.".
- Kolmogorov_backward_equations_(diffusion) label "Equações regressivas de Kolmogorov (difusão)".
- Kolmogorov_backward_equations_(diffusion) label "Kolmogorov backward equations (diffusion)".
- Kolmogorov_backward_equations_(diffusion) sameAs Equações_regressivas_de_Kolmogorov_(difusão).
- Kolmogorov_backward_equations_(diffusion) sameAs m.0g4njc.
- Kolmogorov_backward_equations_(diffusion) sameAs Q3366755.
- Kolmogorov_backward_equations_(diffusion) sameAs Q3366755.
- Kolmogorov_backward_equations_(diffusion) sameAs Kolmogorov_backward_equations_(diffusion).
- Kolmogorov_backward_equations_(diffusion) wasDerivedFrom Kolmogorov_backward_equations_(diffusion)?oldid=566024320.
- Kolmogorov_backward_equations_(diffusion) isPrimaryTopicOf Kolmogorov_backward_equations_(diffusion).