A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise

被引：42
|
作者：
Wang, Xiaojie [1 ]
Gan, Siqing [1 ]
Wang, Desheng [2 ]
机构：
[1] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China
[2] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore
来源：
BIT NUMERICAL MATHEMATICS | 2012年 / 52卷 / 03期
关键词：
Fully implicit Milstein method; Stiff stochastic differential equation; Strong convergence; Mean; square stability; Almost sure asymptotic stability; ASYMPTOTIC STABILITY; NUMERICAL-METHODS; THETA-METHODS; MEAN-SQUARE; SYSTEMS;
D O I：
10.1007/s10543-012-0370-8
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
In this paper a family of fully implicit Milstein methods are introduced for solving stiff stochastic differential equations (SDEs). It is proved that the methods are convergent with strong order 1.0 for a class of SDEs. For a linear scalar test equation with multiplicative noise terms, mean-square and almost sure asymptotic stability of the methods are also investigated. We combine analytical and numerical techniques to get insights into the stability properties. The fully implicit methods are shown to be superior to those of the corresponding semi-implicit methods in term of stability property. Finally, numerical results are reported to illustrate the convergence and stability results.
引用
收藏
页码：741 / 772
页数：32
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