Stability of numerical solution to pantograph stochastic functional differential equations
作者：
Highlights：
• We study a new type of stochastic functional differential equation. The PSFDEs differs markedly from PSDEs, since the current state of PSFDEs depends on a past segment of its solution while the current state of PSDEs depends only on a past point of its solution.
• We are the first to give the definition of the approximate solution for PSFDEs. The approximate solution converges strongly to the analytical solution in finite time interval.
• The numerical solutions preserve the exponential stability and polynomial stability of the analytical solution under the certain conditions.
摘要
•We study a new type of stochastic functional differential equation. The PSFDEs differs markedly from PSDEs, since the current state of PSFDEs depends on a past segment of its solution while the current state of PSDEs depends only on a past point of its solution.•We are the first to give the definition of the approximate solution for PSFDEs. The approximate solution converges strongly to the analytical solution in finite time interval.•The numerical solutions preserve the exponential stability and polynomial stability of the analytical solution under the certain conditions.
论文关键词：Exponential stability,Polynomial stability,Euler–Maruyama,PSFDEs
论文评审过程：Received 12 August 2021, Revised 25 April 2022, Accepted 12 June 2022, Available online 15 June 2022, Version of Record 15 June 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127326
