论文标题
最小化路径测量的相对熵
Minimizing relative entropy of path measures under marginal constraints
论文作者
论文摘要
我们研究了两个方向上统计力学中Schrödinger问题的概括：当密度在两次以上限制时，以及规定粒子的初始和最终位置的联合定律时。这是与最近引入的所谓布丁德问题一致的，以使Brenier的不可压缩流体变异模型正常化。我们在参考度量$ r $相对于解决方案$ p $的radon-nikodym衍生物的标准分解结果的概括概括：该密度可以用在约束时间的集合中编写的添加功能。这项工作的特异性是，我们将自己放在$ r $是马尔可夫（或倒数）的情况下，并且我们使用马尔可夫方法而不是经典的凸分析参数。在这种情况下，似乎在参考度量$ r $上做出的自然假设是不可约性类型的。
We study generalizations of the Schrödinger problem in statistical mechanics in two directions: when the density is constrained at more than two times, and when the joint law of the initial and final positions for the particles is prescribed. This is done in agreement with the so-called Brödinger problem recently introduced to regularize Brenier's variational model for incompressible fluids. We recover generalizations of the standard factorization result for the Radon-Nikodym derivative of the solution $P$ with respect to the reference measure $R$: this density can be written in terms of an additive functional on the set of constrained times. The specificity of this work is that we place ourselves in the case when $R$ is Markov (or reciprocal), and that we use Markovian methods rather than classical convex analysis arguments. In this setting, it appears that a natural assumption to be made on the reference measure $R$ is of irreducibility type.
