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Research on Convergence rates in Machine Learning research part 8

  • We consider Lévy processes that are approximated by compound Poisson processes and, correspondingly, BSDEs driven by Lévy processes that are approximated by BSDEs driven by their compound Poisson approximations.
  • The rate of convergence of the Lévy processes depends on the Blumenthal — Getoor index of the process.
  • We derive the rate of convergence for the BSDEs in the L2-norm and in the Wasserstein distance, and show that, in both cases, this equals the rate of convergence of the corresponding Lévy process, and thus is optimal.
  • We introduce a comprehensive framework for analyzing convergence rates for infinite dimensional linear programming problems (LPs) within the context of the moment-sum-of-squares hierarchy.

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