A revisit of stochastic theta method with some improvements

F. Soleymani; Ali Soheili

doi:10.2298/fil1703585s

A revisit of stochastic theta method with some improvements

Filomat ◽

10.2298/fil1703585s ◽

2017 ◽

Vol 31 (3) ◽

pp. 585-596 ◽

Cited By ~ 1

Author(s):

F. Soleymani ◽

Ali Soheili

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Strong Sense ◽

Stochastic Theta Method ◽

Theta Method

Considering the stochastic theta method, in this work we discuss modified solvers for finding the solution of It? stochastic differential equations in the strong sense. It is observed that the proposed variations are implicit with better stability behaviors. Finally, the derived schemes are tested numerically to confirm the efficiency.

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Asymptotic moment boundedness of the stochastic theta method and its application for stochastic differential equations

Advances in Difference Equations ◽

10.1186/1687-1847-2014-310 ◽

2014 ◽

Vol 2014 (1) ◽

pp. 310 ◽

Cited By ~ 2

Author(s):

Qinwei Qiu ◽

Wei Liu ◽

Liangjian Hu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Moment Boundedness ◽

Stochastic Theta Method ◽

Theta Method

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Choice ofθand mean-square exponential stability in the stochastic theta method of stochastic differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2013.07.007 ◽

2014 ◽

Vol 255 ◽

pp. 837-847 ◽

Cited By ~ 20

Author(s):

Xiaofeng Zong ◽

Fuke Wu

Keyword(s):

Differential Equations ◽

Exponential Stability ◽

Stochastic Differential Equations ◽

Mean Square ◽

Mean Square Exponential Stability ◽

Stochastic Theta Method ◽

Theta Method

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Convergence and stability of stochastic theta method for nonlinear stochastic differential equations with piecewise continuous arguments

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113849 ◽

2021 ◽

pp. 113849

Author(s):

Yuhang Zhang ◽

Minghui Song ◽

Mingzhu Liu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Nonlinear Stochastic Differential Equations ◽

Convergence And Stability ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments ◽

Stochastic Theta Method ◽

Theta Method

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Numerical Approximation of Stochastic Theta Method for Random Periodic Solution of Stochastic Differential Equations

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-020-0959-7 ◽

2020 ◽

Vol 36 (3) ◽

pp. 689-701

Author(s):

Rong Wei ◽

Chuan-zhong Chen

Keyword(s):

Periodic Solution ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Numerical Approximation ◽

Stochastic Theta Method ◽

Theta Method

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Stationary distribution of the stochastic theta method for nonlinear stochastic differential equations

Numerical Algorithms ◽

10.1007/s11075-019-00735-5 ◽

2019 ◽

Vol 83 (4) ◽

pp. 1531-1553 ◽

Cited By ~ 1

Author(s):

Yanan Jiang ◽

Lihui Weng ◽

Wei Liu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Stationary Distribution ◽

Nonlinear Stochastic Differential Equations ◽

Stochastic Theta Method ◽

Theta Method

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Strong convergence rate for multivalued stochastic differential equations via stochastic theta method

Stochastics ◽

10.1080/17442508.2017.1416117 ◽

2017 ◽

Vol 90 (5) ◽

pp. 762-781

Author(s):

Hua Zhang

Keyword(s):

Differential Equations ◽

Convergence Rate ◽

Strong Convergence ◽

Stochastic Differential Equations ◽

Stochastic Theta Method ◽

Strong Convergence Rate ◽

Theta Method

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Convergence and stability of the compensated split-step theta method for stochastic differential equations with piecewise continuous arguments driven by Poisson random measure

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.02.039 ◽

2018 ◽

Vol 340 ◽

pp. 296-317 ◽

Cited By ~ 2

Author(s):

Yulan Lu ◽

Minghui Song ◽

Mingzhu Liu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Random Measure ◽

Poisson Random Measure ◽

Convergence And Stability ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments ◽

Theta Method

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Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2018203 ◽

2019 ◽

Vol 24 (2) ◽

pp. 695-717

Author(s):

Yulan Lu ◽

◽

Minghui Song ◽

Mingzhu Liu

Keyword(s):

Differential Equations ◽

Convergence Rate ◽

Stochastic Differential Equations ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments ◽

Theta Method

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Convergence and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2016.11.033 ◽

2017 ◽

Vol 317 ◽

pp. 55-71 ◽

Cited By ~ 7

Author(s):

Y.L. Lu ◽

M.H. Song ◽

M.Z. Liu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Convergence And Stability ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments ◽

Theta Method

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Stochastic Differential Equations for Power Law Behaviors

10.21236/ada577839 ◽

2012 ◽

Author(s):

Bo Jiang ◽

Roger Brockett ◽

Weibo Gong ◽

Don Towsley

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Power Law

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