Strong convergence of multiscale truncated Euler-Maruyama method for super-linear slow-fast stochastic differential equations

TL;DR

This paper introduces a multiscale Euler-Maruyama method for super-linear slow-fast stochastic differential equations, proving its strong convergence and providing error estimates, supported by numerical simulations.

Contribution

It develops an explicit multiscale Euler-Maruyama scheme with truncation for SFSDEs with locally Lipschitz coefficients, establishing strong convergence and error bounds.

Findings

Proves strong convergence of the proposed scheme.

Provides strong error estimates under mild conditions.

Numerical examples confirm theoretical results.

Abstract

This manuscript is dedicated to the numerical approximation of super-linear slow-fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler-Maruyama scheme suitable for SFSDEs with locally Lipschitz coefficients using an appropriate truncation technique. By the averaging principle, we establish the strong convergence of the numerical solutions to the exact solutions in the pth moment. Additionally, under lenient conditions on the coefficients, we also furnish a strong error estimate. In conclusion, we give two illustrative examples and accompanying numerical simulations to affirm the theoretical outcomes.