STRONG CONVERGENCE IN Lp OF MILSTEIN METHOD FOR ITÔ STOCHASTIC DIFFERENTIAL EQUATIONS

International Journal of Numerical Methods and Applications ◽

10.17654/nm018020031 ◽

2019 ◽

Vol 18 (2) ◽

pp. 31-42

Author(s):

Yazid Alhojilan

Keyword(s):

Differential Equations ◽

Strong Convergence ◽

Stochastic Differential Equations ◽

Milstein Method

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Strong convergence rates of modified truncated EM method for stochastic differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2017.11.024 ◽

2018 ◽

Vol 334 ◽

pp. 1-17 ◽

Author(s):

Guangqiang Lan ◽

Fang Xia

Keyword(s):

Differential Equations ◽

Strong Convergence ◽

Stochastic Differential Equations ◽

Convergence Rates ◽

Em Method ◽

Strong Convergence Rates

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Strong convergence of the stopped Euler–Maruyama method for nonlinear stochastic differential equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2013.08.023 ◽

2013 ◽

Vol 223 ◽

pp. 389-400 ◽

Author(s):

Wei Liu ◽

Xuerong Mao

Keyword(s):

Differential Equations ◽

Strong Convergence ◽

Stochastic Differential Equations ◽

Nonlinear Stochastic Differential Equations

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Strong convergence of split-step backward Euler method for stochastic differential equations with non-smooth drift

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2011.10.023 ◽

2012 ◽

Vol 236 (7) ◽

pp. 1903-1918 ◽

Author(s):

Ali Foroush Bastani ◽

Mahdieh Tahmasebi

Keyword(s):

Differential Equations ◽

Strong Convergence ◽

Stochastic Differential Equations ◽

Euler Method ◽

Backward Euler Method ◽

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Strong convergence and exponential stability of stochastic differential equations with piecewise continuous arguments for non-globally Lipschitz continuous coefficients

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.08.037 ◽

2019 ◽

Vol 341 ◽

pp. 111-127

Author(s):

Huizi Yang ◽

Minghui Song ◽

Mingzhu Liu

Keyword(s):

Differential Equations ◽

Strong Convergence ◽

Exponential Stability ◽

Stochastic Differential Equations ◽

Lipschitz Continuous ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments

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Invariant measures of the Milstein method for stochastic differential equations with commutative noise

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.04.049 ◽

2019 ◽

Vol 358 ◽

pp. 169-176

Author(s):

Lihui Weng ◽

Wei Liu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Invariant Measures ◽

Milstein Method

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Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients

Stochastics ◽

10.1080/17442508.2011.651213 ◽

2012 ◽

Vol 85 (1) ◽

pp. 144-171 ◽

Author(s):

Xuerong Mao ◽

Lukasz Szpruch

Keyword(s):

Differential Equations ◽

Strong Convergence ◽

Stochastic Differential Equations ◽

Diffusion Coefficients ◽

Convergence Rates ◽

Linear Diffusion ◽

Backward Euler ◽

Strong Convergence Rates

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Lp(p>2)-strong convergence of an averaging principle for two-time-scales jump-diffusion stochastic differential equations

Nonlinear Analysis Hybrid Systems ◽

10.1016/j.nahs.2015.05.001 ◽

2015 ◽

Vol 18 ◽

pp. 33-47 ◽

Author(s):

Jie Xu ◽

Yu Miao

Keyword(s):

Differential Equations ◽

Strong Convergence ◽

Stochastic Differential Equations ◽

Time Scales ◽

Jump Diffusion ◽

Averaging Principle

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An improved Milstein method for stiff stochastic differential equations

Advances in Difference Equations ◽

10.1186/s13662-015-0699-9 ◽

2015 ◽

Vol 2015 (1) ◽

Author(s):

Zhengwei Yin ◽

Siqing Gan

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Milstein Method

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Approximation for the solutions of stochastic differential equations: ii strong convergence

Stochastics and Stochastics Reports ◽

10.1080/17442508908833602 ◽

1989 ◽

Vol 28 (4) ◽

pp. 357-385 ◽

Author(s):

Vlad Bally

Keyword(s):

Differential Equations ◽

Strong Convergence ◽

Stochastic Differential Equations

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Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2015.m1208 ◽

2016 ◽

Vol 8 (6) ◽

pp. 1004-1022 ◽

Author(s):

Xu Yang ◽

Weidong Zhao

Keyword(s):

Differential Equations ◽

Theoretical Result ◽

Strong Convergence ◽

Stochastic Differential Equations ◽

Rate Of Convergence ◽

Numerical Experiments ◽

Mean Square ◽

Nonlinear Stochastic Differential Equations ◽

Mean Square Convergence ◽

AbstractIn this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.

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