5 problems

Homotopy multilevel difference bounds. Following a similar derivation as that of the cited corollary and based on the homotopy error bound, the expectation and variance of the mult…

Let $W_k$ denote the Brownian increment, let $H_k$ denote the higher-order stochastic information used by the solver, and let $n_k$ denote the associated discrete random variable.…

Let $\Delta \psi_{\xi,\ell}$ be the correction variables from the naive construction, with $M_\ell=M_0 2^\ell$ and, for $\ell>0$,…

Let $p$ be the polynomial degree of the finite element method basis functions, and consider the variance convergence order of the approximation under the multilevel Monte Carlo sam…

Let $Y_\ell$ be the sparse combination estimator formed from the multilevel samples $Y_{\boldsymbol \ell}$ with $\|{\boldsymbol \ell}\|_1=\ell$. Although substantial cancellation i…