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Is there any paper/book literature on convergence behaviour of solutions to any general or specific BSDE sequences? More precisely, consider the following general problem:

Assume that, for all $n=1,2,\ldots$, we consider a BSDE of the form $$ - \mathrm dY^n_t = f(\cdot,n,t,Y^n_t,Z^n_t) \mathrm dt - Z^n_t \mathrm dW_t $$ with given $Y^n_T = \xi$, where $W$ is a Brownian motion. Then we are interested if there is a convergence $Y^n \to Y^\infty$ (in some sense) as $n \to \infty$.

Any reference to a paper addressing such a problem or a similar problem would be great, thank you.

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