Adaptive Multilevel Monte Carlo for Probabilities

@article{HajiAli2022AdaptiveMM,
  title={Adaptive Multilevel Monte Carlo for Probabilities},
  author={Abdul-Lateef Haji-Ali and Jonathan D. Spence and Aretha L. Teckentrup},
  journal={ArXiv},
  year={2022},
  volume={abs/2107.09148}
}
. We consider the numerical approximation of P [ G ∈ Ω] where the d -dimensional 3 random variable G cannot be sampled directly, but there is a hierarchy of increasingly accurate 4 approximations { G ℓ } ℓ ∈ N which can be sampled. The cost of standard Monte Carlo estimation scales 5 poorly with accuracy in this setup since it compounds the approximation and sampling cost. A direct 6 application of Multilevel Monte Carlo improves this cost scaling slightly, but returns sub-optimal 7… 

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