A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise
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...
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sg-ntu-dr.10356-989932020-03-07T12:34:45Z A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise Wang, Xiaojie Gan, Siqing Wang, Desheng School of Physical and Mathematical Sciences 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. 2013-08-01T01:56:54Z 2019-12-06T20:02:06Z 2013-08-01T01:56:54Z 2019-12-06T20:02:06Z 2012 2012 Journal Article Wang, X., Gan, S.,& Wang, D. (2012). A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise. BIT Numerical Mathematics, 52(3), 741-772. https://hdl.handle.net/10356/98993 http://hdl.handle.net/10220/12699 10.1007/s10543-012-0370-8 en BIT numerical mathematics |
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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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Wang, Xiaojie Gan, Siqing Wang, Desheng |
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Wang, Xiaojie Gan, Siqing Wang, Desheng |
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Wang, Xiaojie Gan, Siqing Wang, Desheng A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise |
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Wang, Xiaojie |
title |
A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise |
title_short |
A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise |
title_full |
A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise |
title_fullStr |
A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise |
title_full_unstemmed |
A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise |
title_sort |
family of fully implicit milstein methods for stiff stochastic differential equations with multiplicative noise |
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2013 |
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https://hdl.handle.net/10356/98993 http://hdl.handle.net/10220/12699 |
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