The truncated θ-Milstein method for nonautonomous and highly nonlinear stochastic differential delay equations

12/21/2021

∙

This paper focuses on the strong convergence of the truncated θ-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate, which is close to one, is given under the weaker assumption than the monotone condition. To verify our theoretical findings, we present a numerical example.

READ FULL TEXT

The truncated θ-Milstein method for nonautonomous and highly nonlinear stochastic differential delay equations

Strong convergence rate of the truncated Euler-Maruyama method for stochastic differential delay equations with Poisson jumps

The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations

Mean-square convergence and stability of the backward Euler method for stochastic differential delay equations with highly nonlinear growing coefficients

Convergence of Numerical Solution of The Tamed Milstein Method for NSDDEs

Convergence rate in ℒ^p sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equations

Convergence and exponential stability of modified truncated Milstein method for stochastic differential equations

Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs

The truncated θ-Milstein method for nonautonomous and highly nonlinear stochastic differential delay equations

Related Research

Strong convergence rate of the truncated Euler-Maruyama method for stochastic differential delay equations with Poisson jumps

The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations

Mean-square convergence and stability of the backward Euler method for stochastic differential delay equations with highly nonlinear growing coefficients

Convergence of Numerical Solution of The Tamed Milstein Method for NSDDEs

Convergence rate in ℒ^p sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equations

Convergence and exponential stability of modified truncated Milstein method for stochastic differential equations

Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs