A study of backward stochastic differential equation on a Riemannian manifold

Xin Chen; Wenjie Ye

A study of backward stochastic differential equation on a Riemannian manifold

Probability 2020-10-07 v1

Authors: Xin Chen , Wenjie Ye

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 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 $N$ .

Keywords

backward stochastic differential equation riemannian manifold global existence local coordinate bsde solution

Cite

@article{arxiv.2010.02465,
  title  = {A study of backward stochastic differential equation on a Riemannian manifold},
  author = {Xin Chen and Wenjie Ye},
  journal= {arXiv preprint arXiv:2010.02465},
  year   = {2020}
}

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