论文标题
在线上的特定相对熵上
On the specific relative entropy between martingale diffusions on the line
论文作者
论文摘要
N. gantert引入的特定相对熵允许量化潜在互惠量度措施的定律之间的差异。它自然而然地表现为Donsker不变性原理的随机版本以及H. Foellmer最近得出的新型传输信息不等式中的大偏差率函数。由上述作者提出的一个猜想涉及封闭形式的表达式，该表达式是连续的martingale法律之间的特定相对熵，其二次变化。我们通过在行为良好的Martingale扩散率的情况下建立这种猜想，从而在这个方向上提供了第一个部分结果。
The specific relative entropy, introduced by N. Gantert, allows to quantify the discrepancy between the laws of potentially mutually singular measures. It appears naturally as the large deviations rate function in a randomized version of Donsker's invariance principle, as well as in a novel transport-information inequality recently derived by H. Foellmer. A conjecture, put forward by the aforementioned authors, concerns a closed form expression for the specific relative entropy between continuous martingale laws in terms of their quadratic variations. We provide a first partial result in this direction, by establishing this conjecture in the case of well-behaved martingale diffusions on the line.
