Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 290, Issue -, Pages 370-384Publisher
ELSEVIER
DOI: 10.1016/j.cam.2015.06.002
Keywords
Stochastic differential equation; Local Lipschitz condition; Khasminskii-type condition; Truncated Euler-Maruyama method; Strong convergence
Categories
Funding
- Leverhulme Trust [RF-2015-385]
- EPSRC [EP/E009409/1]
- Royal Society of London [IE131408]
- Royal Society of Edinburgh [RKES115071]
- London Mathematical Society [11219]
- Edinburgh Mathematical Society [RKES130172]
- Ministry of Education (MOE) of China [MS2014DHDX020]
- EPSRC [EP/E009409/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/E009409/1] Funding Source: researchfish
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Influenced by Higham et al. (2003), several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations (SDEs) under the local Lipschitz condition. These numerical methods include the tamed Euler-Maruyama (EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward EM, etc. In this paper we will develop a new explicit method, called the truncated EM method, for the nonlinear SDE dx(t) = f (x(t))dt + g (x(t))dB(t) and establish the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition x(T)f(x) + p-1/2 vertical bar g(x)vertical bar(2)) <= K (1+ vertical bar x vertical bar(2)). The type of convergence specifically addressed in this paper is strong-L-q convergence for 2 <= q < p, and p is a parameter in the Khasminskii-type condition. (C) 2015 Elsevier B.V. All rights reserved.
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