Multilevel Monte Carlo for Lévy-driven SDEs: central limit theorems for adaptive Euler schemes

DOI10.1214/14-AAP1087zbMath1338.65004arXiv1602.00548OpenAlexW2230749028MaRDI QIDQ259571

Steffen Dereich, Sangmeng Li

Publication date: 11 March 2016

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.00548

zbMATH Keywords

central limit theoremEuler schemestable convergencejump-adapted schemeLévy-driven stochastic differential equationmultilevel Monte Carlo

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Monte Carlo methods (65C05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Numerical solutions to stochastic differential and integral equations (65C30) Finite difference and finite volume methods for ordinary differential equations (65L12)

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Importance sampling and statistical Romberg method for Lévy processes, New methods of simulating Lévy processes, Central limit theorem for the antithetic multilevel Monte Carlo method, Multilevel Monte Carlo Implementation for SDEs Driven by Truncated Stable Processes, Adaptive importance sampling for multilevel Monte Carlo Euler method, General multilevel adaptations for stochastic approximation algorithms. II: CLTs, Central limit theorems for multilevel Monte Carlo methods, Multi-level Monte Carlo methods with the truncated Euler–Maruyama scheme for stochastic differential equations

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