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

Qian Guo; Wei Liu; Xuerong Mao; Weijun Zhan

doi:10.1080/00207160.2017.1329533

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

Qian Guo, Wei Liu, Xuerong Mao, Weijun Zhan

Mathematics And Statistics

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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.

Original language	English
Number of pages	12
Journal	International Journal of Computer Mathematics
Early online date	16 May 2017
DOIs	https://doi.org/10.1080/00207160.2017.1329533
Publication status	E-pub ahead of print - 16 May 2017

Keywords

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

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10.1080/00207160.2017.1329533Licence: CC BY 4.0

Guo-etal-IJCM-2017-Multi-level-Monte-Carlo-methods-with-the-truncated-Euler-MaruyamaFinal published version, 1.03 MBLicence: CC BY 4.0

Cite this

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

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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AU - Liu, Wei

AU - Mao, Xuerong

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PY - 2017/5/16

Y1 - 2017/5/16

N2 - 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.

AB - 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.

KW - truncated Euler-Maruyama method

KW - stochastic differential equations

KW - non-linear coefficients

KW - approximation to expectation

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JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

ER -

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

Abstract

Keywords

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ASYMPTOTIC STABILITY OF NEURAL-TYPE STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

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

Abstract

Keywords

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ASYMPTOTIC STABILITY OF NEURAL-TYPE STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

Cite this