论文标题
与相互作用的向后随机微分方程
Backward Stochastic Differential Equations with interaction
论文作者
论文摘要
在本文中，引入了与相互作用的后向随机微分方程（与相互作用较短的BSDE）。据我们所知，这种方程式在以前没有看到。 BSDE具有相互作用的存在和唯一性结果在Lipschitz条件下与Wasserstein距离有关。当考虑Monge-Kantorovich问题时，自然会出现这种BSDE。在证明中，我们从pardoux和peng的已知结果开始，并通过Wasserstein距离进行近似一般度量。
In this paper backward stochastic differential equations with interaction (shorter BSDEs with interaction) are introduced. Far to our knowledge, this type of equation is not seen in the literature before. Existence and uniqueness result for BSDE with interaction is proved under version of Lipschitz condition with respect to Wasserstein distance. Such kind of BSDE arises naturally when considering Monge-Kantorovich problem. In the proof we start from discrete measures using known result of Pardoux and Peng and approximate general measure via Wasserstein distance.
