2013/12/20 by James MacLaurin, MacLaurin, James, Olivier Faugeras +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories #math.PR
paper · pdf · doi:10.48550/arxiv.1312.5888
openalex publication_date 2013/12/20 · arxiv created 2014/04/18 · arxiv updated 2014/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback-Leibler Divergence) between measures mu and P on the space of continuous functions from time 0 to T. The underlying measure P is a weak solution to a Martingale Problem with continuous coefficients. Since the relative entropy governs the exponential rate of convergence of the empirical measure (according to Sanov's Theorem), this representation is of use in the numerical and analytical investigation of finite-size effects in systems of interacting diffusions.