Analysis of nested multilevel Monte Carlo using approximate Normal random variables
arXiv:2102.08164 · doi:10.1137/21M1399385
Abstract
The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables which can be computed much more cheaply. A nested MLMC approach is adopted in which a two-level treatment of the approximated random variables is embedded within a standard MLMC application. We analyse the resulting nested MLMC variance in the specific context of an SDE discretisation in which Normal random variables can be replaced by approximately Normal random variables, and provide numerical results to support the analysis.
arXiv comment24 pages, 2 figures
References in corpus (6)
- Multilevel Sequential Monte Carlo Samplers
- Multilevel ensemble Kalman filtering
- Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation
- A multilevel Monte Carlo method for computing failure probabilities
- Decision-making under uncertainty: using MLMC for efficient estimation of EVPPI
- Approximating inverse cumulative distribution functions to produce approximate random variables