On the form of the large deviation rate function for the empirical measures of weakly interacting systems
On the form of the large deviation rate function for the empirical measures of weakly interacting systems
复制标题
弱相互作用系统经验测度大偏差率函数的形式
DOI：
10.3150/13-bej540
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Markus Fischer
中科院分区：
文献类型：
--
作者：
Markus Fischer
大偏差理论的一个基本结果是Sanov定理，它指出独立同分布样本的经验测度序列满足大偏差原理，其速率函数由相对熵关于共同分布给出。大偏差原则的经验措施也被称为持有广泛类弱相互作用系统。当通过经验测度的相互作用对应于测度的绝对连续变化时，速率函数可以表示为相对于McKean-Vlasov极限定律的分布的相对熵，其中测度变量冻结在该分布处。我们讨论的情况下，超出倾斜分布，其中一个大的偏差原则持有率函数的相对熵的形式。
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by relative entropy with respect to the common distribution. Large deviation principles for the empirical measures are also known to hold for broad classes of weakly interacting systems. When the interaction through the empirical measure corresponds to an absolutely continuous change of measure, the rate function can be expressed as relative entropy of a distribution with respect to the law of the McKean-Vlasov limit with measure-variable frozen at that distribution. We discuss situations, beyond that of tilted distributions, in which a large deviation principle holds with rate function in relative entropy form.