Suppose N is a compact Riemannian manifold, in this paper we will introduce the definition of N-valued BSDE and -valued BSDE for which the solutions are not necessarily staying in only one local coordinate. Moreover, the global existence of a solution to -valued BSDE will be proved without any convexity condition on N.
The research of Xin Chen and Wenjie Ye is supported by the National Natural Science Foundation of China (No. 11871338).
"A study of backward stochastic differential equation on a Riemannian manifold." Electron. J. Probab. 26 1 - 31, 2021. https://doi.org/10.1214/21-EJP649