Stability of Tamed EM scheme of Neutral Stochastic Differential Delay Equations

TL;DR

This paper investigates the stability properties of the tamed Euler-Maruyama scheme applied to neutral stochastic differential delay equations, revealing that mean-square stability implies almost sure stability without additional conditions.

Contribution

It demonstrates that exponential mean-square stability of the scheme guarantees almost sure stability, a novel insight for neutral stochastic delay equations.

Findings

Exponential mean-square stability implies almost sure stability.

The tamed EM scheme effectively preserves stability properties.

No extra conditions are needed for stability transfer.

Abstract

In this paper, exponential mean-square stability and almost sure stability of the tamed EM scheme to neutral stochastic differential delay equation are investigated. Surprisingly, the exponential mean-square stability can reproduce the almost sure stability without placing extra conditions.