Analysis of nested multilevel Monte Carlo using approximate Normal random variables

TL;DR

This paper explores a nested multilevel Monte Carlo method that replaces Normal random variables with approximate versions to reduce computational cost, analyzing variance and demonstrating effectiveness through numerical experiments.

Contribution

It introduces a nested MLMC approach for approximate Normal variables within SDE discretization, providing variance analysis and numerical validation.

Findings

Nested MLMC reduces computational cost.

Variance analysis supports efficiency claims.

Numerical results confirm theoretical predictions.

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.