The truncated Milstein method for super-linear stochastic differential equations with Markovian switching

DOI10.3934/dcdsb.2021201zbMath1498.60293OpenAlexW3192220264WikidataQ115219177 ScholiaQ115219177MaRDI QIDQ2090322

Qian Guo, Yuhao Cong, Weijun Zhan

Publication date: 25 October 2022

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2021201

zbMATH Keywords

stochastic differential equationstrong convergenceMarkovian switchingKhasminskii-type conditionMilstein method

Mathematics Subject Classification ID

Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (2)

Convergence and stability of the Milstein scheme for stochastic differential equations with piecewise continuous arguments ⋮ Unnamed Item

Cites Work

• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• The truncated Euler-Maruyama method for stochastic differential equations
• Strong convergence and stability of backward Euler-Maruyama scheme for highly nonlinear hybrid stochastic differential delay equation
• Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations
• Convergence of the Euler--Maruyama method for stochastic differential equations with Markovian switching.
• The truncated Milstein method for stochastic differential equations with commutative noise
• Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
• Milstein-Type Procedures for Numerical Solutions of Stochastic Differential Equations with Markovian Switching
• A Fundamental Mean-Square Convergence Theorem for SDEs with Locally Lipschitz Coefficients and Its Applications
• Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment and stability

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