The partially truncated Euler-Maruyama method and its stability and boundedness

Qian Guo; Wei Liu; Xuerong Mao; Rongxian Yue

The partially truncated Euler-Maruyama method and its stability and boundedness

Qian Guo, Wei Liu, Xuerong Mao, Rongxian Yue

Mathematics And Statistics

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Abstract

The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will not
only establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method by
showing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs.

Original language	English
Journal	Applied Numerical Mathematics
Publication status	Accepted/In press - 23 Jan 2017

Keywords

Stochastic differential equations
local Lipschitz condition
Khasminskii-type condition
partially truncated Euler-Maruyama method
stability
boundedness

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Guo-etal-ANM2017-Partially-truncated-Euler-Maruyama-method-and-its-stability-and-boundednessAccepted author manuscript, 433 KBLicence: CC BY-NC-ND 4.0

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title = "The partially truncated Euler-Maruyama method and its stability and boundedness",

abstract = "The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will notonly establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method byshowing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs.",

keywords = "Stochastic differential equations, local Lipschitz condition, Khasminskii-type condition, partially truncated Euler-Maruyama method, stability, boundedness",

author = "Qian Guo and Wei Liu and Xuerong Mao and Rongxian Yue",

year = "2017",

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T1 - The partially truncated Euler-Maruyama method and its stability and boundedness

AU - Guo, Qian

AU - Liu, Wei

AU - Mao, Xuerong

AU - Yue, Rongxian

PY - 2017/1/23

Y1 - 2017/1/23

N2 - The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will notonly establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method byshowing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs.

AB - The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will notonly establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method byshowing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs.

KW - Stochastic differential equations

KW - local Lipschitz condition

KW - Khasminskii-type condition

KW - partially truncated Euler-Maruyama method

KW - stability

KW - boundedness

UR - http://www.sciencedirect.com/science/journal/01689274

M3 - Article

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -

The partially truncated Euler-Maruyama method and its stability and boundedness

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Keywords

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