Abstract
Language | English |
---|---|
Pages | 157-170 |
Number of pages | 14 |
Journal | Applied Numerical Mathematics |
Volume | 130 |
Early online date | 11 Apr 2018 |
DOIs | |
Publication status | Published - 31 Aug 2018 |
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Keywords
- stochastic differential equationquation
- local Lipschitz condition
- Khasminskii-type condition
- partially truncated Euler–Maruyama method
- convergence rate
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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
TY - JOUR
T1 - A note on the partially truncated Euler–Maruyama method
AU - Guo, Qian
AU - Liu, Wei
AU - Mao, Xuerong
PY - 2018/8/31
Y1 - 2018/8/31
N2 - 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 LT-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 LT-convergence rate. The advantages of our new results will be highlighted by the comparisons with our earlier results in [3].
AB - 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 LT-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 LT-convergence rate. The advantages of our new results will be highlighted by the comparisons with our earlier results in [3].
KW - stochastic differential equationquation
KW - local Lipschitz condition
KW - Khasminskii-type condition
KW - partially truncated Euler–Maruyama method
KW - convergence rate
UR - https://www.sciencedirect.com/journal/applied-numerical-mathematics
U2 - 10.1016/j.apnum.2018.04.004
DO - 10.1016/j.apnum.2018.04.004
M3 - Article
VL - 130
SP - 157
EP - 170
JO - Applied Numerical Mathematics
T2 - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
ER -