Stabilized explicit methods for the approximation of stochastic systems driven by small additive noises

被引：5
作者：
de la Cruz, H. [1 ]
机构：
[1] Fundacao Getulio Vargas, Sch Appl Math, Rio De Janeiro, Brazil
来源：
CHAOS SOLITONS & FRACTALS | 2020年 / 140卷
关键词：
Stochastic differential equations; Stability; Small noises; Computer simulation; Local linearization approach; Additive noise; RUNGE-KUTTA METHODS; DIFFERENTIAL-EQUATIONS; NUMERICAL-METHODS; SIMULATION;
D O I：
10.1016/j.chaos.2020.110195
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop an approach for the construction of stable numerical schemes for the strong approximation of stochastic differential systems with small additive noises. Explicit integrators with valuable stability properties are proposed and their mean-square convergence is studied. Computer simulations are carry out to illustrate the practical performance of the methods and their advantages in comparison with other existing integrators. (c) 2020 Elsevier Ltd. All rights reserved.
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页数：12
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共 31 条
  • [1] [Anonymous], 2019, MATRIX DIFFERENTIAL, DOI DOI 10.1002/9781119541219.CH18
  • [2] Arnold L., 1974, Stochastic differential equations
  • [3] Artemiev S.S., 1997, Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations
  • [4] BUCKWAR E, 2004, PAMM, V4, P15
  • [5] Multistep methods for SDES and their application to problems with small noise
    Buckwar, Evelyn
    Winkler, Renate
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (02) : 779 - 803
  • [6] STOCHASTIC RUNGE-KUTTA METHODS FOR ITO SODEs WITH SMALL NOISE
    Buckwar, Evelyn
    Roessler, Andreas
    Winkler, Renate
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (04) : 1789 - 1808
  • [7] Numerical methods for second-order stochastic differential equations
    Burrage, Kevin
    Lenane, Ian
    Lythe, Grant
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2007, 29 (01) : 245 - 264
  • [8] Clark J.M.C., 1980, Stochastic differential systems filtering and control, P162
  • [9] High order local linearization methods: An approach for constructing A-stable explicit schemes for stochastic differential equations with additive noise
    De la Cruz Cancino, H.
    Biscay, R. J.
    Jimenez, J. C.
    Carbonell, F.
    Ozaki, T.
    [J]. BIT NUMERICAL MATHEMATICS, 2010, 50 (03) : 509 - 539
  • [10] Locally Linearized methods for the simulation of stochastic oscillators driven by random forces
    de la Cruz, H.
    Jimenez, J. C.
    Zubelli, J. P.
    [J]. BIT NUMERICAL MATHEMATICS, 2017, 57 (01) : 123 - 151
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