A note on the partially truncated Euler–Maruyama method

Qian Guo; Wei Liu; Xuerong Mao

doi:10.1016/j.apnum.2018.04.004

A note on the partially truncated Euler–Maruyama method

Qian Guo, Wei Liu, Xuerong Mao

Mathematics And Statistics

Research output: Contribution to journal › Article

4 Citations (Scopus)

Abstract

The partially truncated Euler–Maruyama (EM) method was recently proposed in our earlier paper [3] for highly nonlinear stochastic differential equations (SDEs), where the finite-time strong L^T-convergence theory was established. In this note, we will point out that one condition imposed there is restrictive in the sense that this condition might force the stepsize to be so small that the partially truncated EM method would be inapplicable. In this note, we will remove this restrictive condition but still be able to establish the finite-time strong L^T-convergence rate. The advantages of our new results will be highlighted by the comparisons with our earlier results in [3].

Language	English
Pages	157-170
Number of pages	14
Journal	Applied Numerical Mathematics
Volume	130
Early online date	11 Apr 2018
DOIs	10.1016/j.apnum.2018.04.004
Publication status	Published - 31 Aug 2018

Fingerprint

Euler-Maruyama Method

Differential equations

Strong Convergence

Convergence Theory

Stochastic Equations

Convergence Rate

Differential equation

Keywords

stochastic differential equationquation
local Lipschitz condition
Khasminskii-type condition
partially truncated Euler–Maruyama method
convergence rate

Cite this

Guo, Q., Liu, W., & Mao, X. (2018). A note on the partially truncated Euler–Maruyama method. Applied Numerical Mathematics, 130, 157-170. https://doi.org/10.1016/j.apnum.2018.04.004

Guo, Qian ; Liu, Wei ; Mao, Xuerong. / A note on the partially truncated Euler–Maruyama method. In: Applied Numerical Mathematics. 2018 ; Vol. 130. pp. 157-170.

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Guo, Q, Liu, W & Mao, X 2018, 'A note on the partially truncated Euler–Maruyama method' Applied Numerical Mathematics, vol. 130, pp. 157-170. https://doi.org/10.1016/j.apnum.2018.04.004

A note on the partially truncated Euler–Maruyama method. / Guo, Qian; Liu, Wei; Mao, Xuerong.

In: Applied Numerical Mathematics, Vol. 130, 31.08.2018, p. 157-170.

Research output: Contribution to journal › Article

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AU - Liu, Wei

AU - Mao, Xuerong

PY - 2018/8/31

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KW - stochastic differential equationquation

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