Abstract
The Euler–Maruyama method is presented for linear stochastic Volterra integral equations. Then the strong convergence property is analyzed for convolution kernels and general kernels, respectively. It is well known that for stochastic ordinary differential equations, the strong convergence order of the Euler–Maruyama method is 12. However, the strong superconvergence order of 1 is obtained for linear stochastic Volterra integral equations with convolution kernels if the kernel K2 of the diffusion term satisfies K2(0)=0; and this strong superconvergence property is inherited by linear stochastic Volterra integral equations with general kernels if the kernel K2 of the diffusion term satisfies K2(t,t)=0. The theoretical results are illustrated by extensive numerical examples.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
