Strong convergence of explicit schemes for highly nonlinear stochastic differential equations with Markovian switching
作者：
Highlights：
• Base on a novel approach which only involves the exact solution process, we analyze mean square convergence of two explicit methods for highly nonlinear stochastic differential equations with Markov switching (SDEMS).
• Under the global monotone condition, we prove two explicit methods are mean square convergent with order 0.5 for highly nonlinear SDEMS.
• For highly nonlinear stochastic differential equations with small noise, two explicit methods can keep convergence properties of the corresponding deterministic schemes under certain condition.
• For highly nonlinear SDEMS with small noise, two explicit methods can both mean square converge at rate 1.
摘要
•Base on a novel approach which only involves the exact solution process, we analyze mean square convergence of two explicit methods for highly nonlinear stochastic differential equations with Markov switching (SDEMS).•Under the global monotone condition, we prove two explicit methods are mean square convergent with order 0.5 for highly nonlinear SDEMS.•For highly nonlinear stochastic differential equations with small noise, two explicit methods can keep convergence properties of the corresponding deterministic schemes under certain condition.•For highly nonlinear SDEMS with small noise, two explicit methods can both mean square converge at rate 1.
论文关键词：Stochastic differential equation,Markov process,Monotone condition,Mean square convergence,Small noise
论文评审过程：Received 23 October 2020, Revised 2 January 2021, Accepted 3 January 2021, Available online 30 January 2021, Version of Record 30 January 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.125959
