Strong convergence rate of the stochastic theta method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments

DOI10.1007/s40314-022-02089-6OpenAlexW4307991211WikidataQ115373125 ScholiaQ115373125MaRDI QIDQ2099521

Minghui Song, Bowen Zhao, YuHang Zhang, Ming-Zhu Liu

Publication date: 24 November 2022

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-022-02089-6

zbMATH Keywords

convergence rateforward-backward Euler-Maruyama (FBEM) methodstochastic differential equations with piecewise continuous arguments (SDEPCAs)stochastic theta (ST) method

Mathematics Subject Classification ID

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

Cites Work

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• Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations
• A Taylor polynomial approach in approximations of solution to pantograph stochastic differential equations with Markovian switching
• Convergence of the semi-implicit Euler method for neutral stochastic delay differential equations with phase semi-Markovian switching
• Compensated split-step balanced methods for nonlinear stiff SDEs with jump-diffusion and piecewise continuous arguments
• Convergence of numerical solution to stochastic delay differential equation with Poisson jump and Markovian switching
• Approximations of Euler-Maruyama type for stochastic differential equations with Markovian switching, under non-Lipschitz conditions
• Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching
• Hybrid switching diffusions. Properties and applications
• Convergence of the Euler--Maruyama method for stochastic differential equations with Markovian switching.
• Almost sure exponential stability of hybrid stochastic functional differential equations
• Existence and exponential stability of solutions for stochastic cellular neural networks with piecewise constant argument
• Backward Euler-Maruyama method applied to nonlinear hybrid stochastic differential equations with time-variable delay
• Switching-dominated stability of numerical solutions for hybrid neutral stochastic differential delay equations
• Stabilisation of highly nonlinear hybrid stochastic differential delay equations by delay feedback control
• Convergence of numerical solutions to stochastic differential delay equations with Poisson jump and Markovian switching
• Convergence and stability of numerical solutions to SDDEs with Markovian switching
• Modeling and Analysis of Switching Diffusion Systems: Past-Dependent Switching with a Countable State Space
• Option Pricing With Markov-Modulated Dynamics
• Advances in Stabilization of Hybrid Stochastic Differential Equations by Delay Feedback Control
• Stabilization of Hybrid Systems by Feedback Control Based on Discrete-Time State Observations
• Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients
• Stochastic Differential Equations with Markovian Switching
• The Numerical Invariant Measure of Stochastic Differential Equations With Markovian Switching