|
In mathematics, specifically in the theory of Markovian stochastic processes in probability theory, the Chapman–Kolmogorov equation is an identity relating the joint probability distributions of different sets of coordinates on a stochastic process. The equation was arrived at independently by both the British mathematician Sydney Chapman and the Russian mathematician Andrey Kolmogorov. == Mathematical description == Suppose that is an indexed collection of random variables, that is, a stochastic process. Let : be the joint probability density function of the values of the random variables ''f''1 to ''fn''. Then, the Chapman–Kolmogorov equation is : i.e. a straightforward marginalization over the nuisance variable. (Note that we have not yet assumed anything about the temporal (or any other) ordering of the random variables — the above equation applies equally to the marginalization of any of them.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Chapman–Kolmogorov equation」の詳細全文を読む スポンサード リンク
|