
Review of Short Phrases and Links 
This Review contains major "ChapmanKolmogorov Equation" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 A ChapmanKolmogorov equation is a necessary but not sufficient condition for a Markov process.
ChapmanKolmogorov Equation
 A conditional probability with initial state memory is not guaranteed to obey a ChapmanKolmogorov equation and usually doesn't.
 When the stochastic process under consideration is Markovian, the ChapmanKolmogorov equation is equivalent to an identity on transition densities.
 Using fractional integrals, we derive the fractional generalization of the ChapmanKolmogorov equation (Smolukhovski equation).
 In this paper fractional FokkerPlanck equation for fractal media is derived from the fractional ChapmanKolmogorov equation.

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