In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback–Leibler Divergence) R(μ||P), where μ and P are measures on C([0, T]; ℝd). The underlying measure P is a weak solution to a martingale problem with continuous coefficients. Our representation is in the form of an integral with respect to its infinitesimal generator. This representation is of use in statistical inference (particularly involving medical imaging). Since R(μ||P) governs the exponential rate of convergence of the empirical measure (according to Sanov’s theorem), this representation is also of use in the numerical and analytical investigation of finite-size effects in systems of interacting diffusions.
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机译：在本文中，我们得出相对熵（或Kullback-Leibler发散度）R（μ|| P）的积分（相对于时间）表示，其中μ和P是对C（[0，T];ℝ< sup> d ）。。基础度量P是具有连续系数的mar问题的弱解。关于其无穷小生成器，我们以积分的形式表示。此表示形式可用于统计推断（特别是涉及医学成像）。由于R（μ|| P）控制着经验测度的指数收敛速度（根据Sanov定理），因此该表示形式也可用于相互作用扩散系统中有限尺寸效应的数值和分析研究。
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