|
In the study of stochastic processes, an adapted process (or non-anticipating process) is one that cannot "see into the future". An informal interpretation is that ''X'' is adapted if and only if, for every realisation and every ''n'', ''Xn'' is known at time ''n''. The concept of an adapted process is essential, for instance, in the definition of the Itō integral, which only makes sense if the integrand is an adapted process. ==Definition== Let * be a probability space; * be an index set with a total order (often, is , , or ); * be a filtration of the sigma algebra ; * be a measurable space, the ''state space''; * be a stochastic process. The process is said to be adapted to the filtration if the random variable is a -measurable function for each . 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「adapted process」の詳細全文を読む スポンサード リンク
|