A study of backward stochastic differential equation on a Riemannian manifold

Xin Chen; Wenjie Ye

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arXiv · 2010.02465

A study of backward stochastic differential equation on a Riemannian manifold

Xin Chen·Wenjie Ye

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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 $N$.

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Xin Chen, Wenjie Ye. 2020-10-06. A study of backward stochastic differential equation on a Riemannian manifold. https://arxiv.org/abs/2010.02465

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