Multilevel Monte Carlo methods
Michael B. Giles
TL;DR
This paper reviews the development of multilevel Monte Carlo methods since 2006, highlighting their simplicity, flexibility, and potential for future research in stochastic simulation.
Contribution
It provides an overview of progress in multilevel Monte Carlo methods, introduces new ideas, and discusses future research directions.
Findings
Significant research progress since 2006
Enhanced understanding of method flexibility and simplicity
Identification of promising future research areas
Abstract
The author's presentation of multilevel Monte Carlo path simulation at the MCQMC 2006 conference stimulated a lot of research into multilevel Monte Carlo methods. This paper reviews the progress since then, emphasising the simplicity, flexibility and generality of the multilevel Monte Carlo approach. It also offers a few original ideas and suggests areas for future research.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Statistical Methods and Inference · Mathematical Approximation and Integration