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Stability of numerical method for semi-linear stochastic pantograph differential equations

Yu Zhang, Longsuo Li
2016 Journal of Inequalities and Applications  
Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution  ...  In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations.  ...  Euler-Maruyama method can reproduce almost surely exponential stability for highly nonlinear stochastic pantograph differential equations.  ... 
doi:10.1186/s13660-016-0971-x fatcat:ao6mkie32nczhazbevcu6gyzjm

Numerical approximation for nonlinear stochastic pantograph equations with Markovian switching

Shaobo Zhou, Yangzi Hu
2016 Applied Mathematics and Computation  
The main aim of the paper is to prove that the implicit numerical approximation can converge to the true solution to highly nonlinear hybrid stochastic pantograph differential equation.  ...  Zhou et al. [22] studied convergence in probability of the Euler-Maruyama approximate solution of stochastic pantograph differential equation.  ...  Research efforts have been devoted to existence-and-uniqueness and stability of the analytical solution for stochastic pantograph equation [1, 2, 16] .  ... 
doi:10.1016/j.amc.2016.03.040 fatcat:fpdeoin74rh4nca5uus6bomk6m

Stability of Numerical Solution to Pantograph Stochastic Functional Differential Equations [article]

Hao Wu, Junhao Hu, Chenggui Yuan
2021 arXiv   pre-print
In this paper, we study the convergence of the Euler-Maruyama numerical solutions for pantograph stochastic functional differential equations which was proposed in [11].  ...  We also show that the numerical solutions have the properties of almost surely polynomial stability and exponential stability with the help of semi-martingale convergence theorem.  ...  For example, Milošević [7] studied existence, uniqueness and almost sure polynomial stability of solution to a class of highly nonlinear PSDEs and the Euler-Maruyama (EM) approximation. Shen et al.  ... 
arXiv:2108.01248v1 fatcat:jxp4jldbqzgapebbrqbezz6dnm

On the approximations of solutions to stochastic differential equations under polynomial condition

Dusan Djordjevic, Miljana Jovanovic
2021 Filomat  
The subject of this paper is an analytic approximate method for a class of stochastic differential equations with coefficients that do not necessarily satisfy the Lipschitz and linear growth conditions  ...  More precisely, equations from the observed class have unique solutions with bounded moments and their coefficients satisfy polynomial condition.  ...  In that way, we extend the results from [12] to a class of stochastic differential equations with drift coefficients which could be highly nonlinear.  ... 
doi:10.2298/fil2101011d fatcat:toxvhh6pjzh5fexwajydgv5lui