Two end points marginal problem by stochastic optimal transportation
Two end points marginal problem by stochastic optimal transportation
复制标题
随机最优运输的两个端点边际问题
DOI：
10.1137/14099070x
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Toshio Mikami
中科院分区：
文献类型：
--
作者：
白川健;渡邉紘;S.Moll;Yuichi Shiozawa;Mikio Kato;渡邉紘;渡邉紘;塩沢 裕一;Toshio Mikami
给出了随机最优运输问题是有限的一个充分条件，该条件包含了具有给定初始分布和终端分布的半鞅的存在性。证明的思想是证明随机最优运输问题对偶定理中上确界的有限性。作为特殊情况，给出了给定初始分布和终端分布的h-路过程的构造方法。我们还考虑了一类Fokker-Planck方程族解的最优控制问题。
We give a sufficient condition under which the stochastic optimal transportation problem is finite, which implies the existence of a semimartingale with given initial and terminal distributions. The idea of the proof is to show the finiteness of the supremum in the duality theorem for the stochastic optimal transportation problem. As a special case, it also gives a new approach for the construction of the h-path process with given initial and terminal distributions. We also consider a problem similar to the above for a class of optimal control problems for a family of solutions to Fokker--Planck equations.