The logarithmic derivative of a weakly second order probability measure mu on a general vector space X is an example of an operator from X into L(2)(mu) which preserves the pairing of X and X' under the inner product of L(2)(mu). This biorthogonality property is exploited to obtain. by means of comparison, a lower bound on mu's covariance operator. nle logarithmic derivative is then explicitly evaluated for probability measures induced by the solutions to stochastic ordinary and partial differential equations. (C) 1996 Academic Press. Inc. [References: 23]
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机译：一般向量空间X上的弱二阶概率测度mu的对数导数是从X到L（2）（mu）的算子的一个示例，该算子在X（2）的内积下保留了X和X'的对）（亩）。利用这种生物正交性来获得。通过比较，亩的协方差算子的下限。然后，对数对数导数进行明确评估，以评估由随机微分方程和偏微分方程解引起的概率测度。 （C）1996年学术出版社。 Inc. [参考：23]
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