Multi-level Monte Carlo methods with the truncated Euler-Maruyama scheme for stochastic differential equations

Qian Guo, Wei Liu, Xuerong Mao, Weijun Zhan

Research output: Contribution to journalArticle

Abstract

The truncated Euler-Maruyama method is employed together with the Multi-level Monte Carlo method to approximate expectations of some functions of solutions to stochastic differential equations (SDEs). The convergence rate and the computational cost of the approximations are proved, when the coefficients of SDEs satisfy the local Lipschitz and Khasminskii-type conditions. Numerical examples are provided to demonstrate the theoretical results.
LanguageEnglish
Number of pages12
JournalInternational Journal of Computer Mathematics
Early online date16 May 2017
DOIs
Publication statusE-pub ahead of print - 16 May 2017

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Multilevel Methods
Monte Carlo method
Stochastic Equations
Euler
Differential equations
Monte Carlo methods
Euler-Maruyama Method
Differential equation
Lipschitz
Convergence Rate
Computational Cost
Numerical Examples
Coefficient
Approximation
Demonstrate
Costs

Keywords

  • truncated Euler-Maruyama method
  • stochastic differential equations
  • non-linear coefficients
  • approximation to expectation

Cite this

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abstract = "The truncated Euler-Maruyama method is employed together with the Multi-level Monte Carlo method to approximate expectations of some functions of solutions to stochastic differential equations (SDEs). The convergence rate and the computational cost of the approximations are proved, when the coefficients of SDEs satisfy the local Lipschitz and Khasminskii-type conditions. Numerical examples are provided to demonstrate the theoretical results.",
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