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The monotonicity condition for BSDE on manifolds

Fabrice Blache
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Abstract

In two preceding articles, we studied the problem of the existence and uniqueness of a solution to some general BSDE on manifolds. In these two articles, we assumed some Lipschitz conditions on the drift $f(b,x,z)$. The purpose of this article is to extend the existence and uniqueness results under weaker assumptions, in particular a monotonicity condition in the variable $x$. This extends well-known results for Euclidean BSDE.

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Fabrice Blache. 2005-12-16. The monotonicity condition for BSDE on manifolds. https://arxiv.org/abs/math/0512403

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