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In probability theory, the Wick product is a particular way of defining an adjusted product of a set of random variables. In the lowest order product the adjustment corresponds to subtracting off the mean value, to leave a result whose mean is zero. For the higher order products the adjustment involves subtracting off lower order (ordinary) products of the random variables, in a symmetric way, again leaving a result whose mean is zero. The Wick product is a polynomial function of the random variables, their expected values, and expected values of their products. The definition of the Wick product immediately leads to the Wick power of a single random variable and this allows analogues of other functions of random variables to be defined on the basis of replacing the ordinary powers in a power-series expansions by the Wick powers. The Wick product is named after physicist Gian-Carlo Wick, cf. Wick's theorem. ==Definition== The Wick product, : is a sort of product of the random variables, ''X''1, ..., ''X''''k'', defined recursively as follows: : (i.e. the empty product—the product of no random variables at all—is 1). Thereafter finite moments must be assumed. Next, for ''k''≥1, : where means ''X''''i'' is absent, and the constraint that : 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「Wick product」の詳細全文を読む スポンサード リンク
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