Central Limit Theorem for Irregular Discretization Scheme of Multilevel Monte Carlo Method

2025/02/20 by Yi Guo, Guo, Yi, Yuxi Guo +3
Engineering · #FOS: Mathematics #Probability (math.PR) #Radiative Heat Transfer Studies

paper · pdf · doi:10.48550/arxiv.2502.14395

openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the asymptotic error distribution for a two-level irregular discretization scheme of the solution to the stochastic differential equations (SDE for short) driven by a continuous semimartingale and obtain a central limit theorem for the error processes with the rate √(n). As an application, in the spirit of the result of Ben Alaya and Kebaier, we get a central limit theorem of the Linderberg-Feller type for the irregular discretization scheme of the multilevel Monte Carlo method.

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