Definition
In probability theory, Kolmogorov equations characterize continuous-time Markov processes. In particular, they describe how the probability of a continuous-time Markov process in a certain state changes over time. There are four distinct equations: the Kolmogorov forward equation for continuous processes, now understood to be identical to the Fokker–Planck equation, the Kolmogorov forward equation for jump processes, and two Kolmogorov backward equations for processes with and without discontinuous jumps.
Related concepts
Andrey KolmogorovAnnals of MathematicsBirth rateBrownian motionChapman–Kolmogorov equationContinuous-time Markov processCountable setDiffusionFeynman–Kac formulaFokker–Planck equationItô diffusionJump processKolmogorov backward equationKolmogorov backward equations (diffusion)Kolmogorov equations (Markov jump process)Kolmogorov population modelMarkov processMaster equationMathematische AnnalenMotoo KimuraPartial differential equationPopulation sizeProbabilityProbability theoryTransition rate matrixWilliam Feller
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