Strong Convergence Order of the Projected Euler-Maruyama Method for Neutral Stochastic Delay Differential Equations Under a Global Monotone Condition

Abstract

This paper is concerned with the strong convergence of the projected Euler-Maruyama (PEM) method for neutral stochastic delay differential equations (NSDDEs) with variable delays. First, the notions of C-stability and B-consistency are defined for NSDDEs. Subsequently, under a global monotone condition, a fundamental theorem on strong convergence is established for general one-step methods applied to nonlinear NSDDEs. We then construct the PEM method, an explicit one-step scheme, and prove its C-stability, B-consistency, and strong convergence of order 1/2. Finally, a numerical experiment is presented to validate the results.

Keywords

Neutral stochastic delay differential equations (NSDDEs) / Strong convergence / Projected Euler-Maruyama (PEM) method / C-stability / B-consistency / Non-global Lipschitz condition / 65C20 / 65L20 / 60H35

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Funding

the Key Research Program of Higher Education Institutions of Henan Province(24B110019)

RIGHTS & PERMISSIONS

Shanghai University

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