论文标题
对riemannian歧管上向后随机微分方程的研究
A study of backward stochastic differential equation on a Riemannian manifold
论文作者
论文摘要
假设$ n $是一种紧凑的riemannian歧管，在本文中，我们将介绍$ n $值的bsde和$ l^2的定义（\ mathbb {t}^m; n）$ - 有价值的BSDE，该解决方案不一定仅保留在一个本地坐标中。此外，将证明$ l^2（\ mathbb {t}^m; n）$ - 有价值的bsde的全球存在解决方案将在$ n $上没有任何凸状条件证明。
Suppose $N$ is a compact Riemannian manifold, in this paper we will introduce the definition of $N$-valued BSDE and $L^2(\mathbb{T}^m;N)$-valued BSDE for which the solution are not necessarily staying in only one local coordinate. Moreover, the global existence of a solution to $L^2(\mathbb{T}^m;N)$-valued BSDE will be proved without any convexity condition on $N$.
