Deep BSDE Solver on Bounded Domains Part I: General Loss Rate

We consider a ramification of the deep BSDE loss functional designed to apply for BSDEs on bounded domains, i.e. with random (unbounded) time horizons. We derive a general convergence rate of the loss functional; precisely for a class of (randomly) weighted modifications of the functional. The rate is expressed in terms of the underlying discrete-time stepsize and a universal approximation distance.