A study of backward stochastic differential equation on a Riemannian manifold

Abstract

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 solutions 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.