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What is MLMC Complexity and Variance Reduction about?

The MLMC complexity theorem shows that under certain conditions, the MLMC method can reduce the complexity of estimating expectations compared to standard MC. If the variance decreases faster than the cost increases (β > γ), MLMC has complexity O(ε-2). If they decrease at the same rate (β = γ), complexity is O(ε-2(logε)2). If variance decreases slower than cost (β < γ), complexity is O(ε-2-β/α). To achieve a target accuracy ε, the number of samples N` and levels L must be chosen to control the variance and

Author

Kaveh Ara

Language

EN