Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations

الملخص EN

We investigate the almost surely asymptotic stability of Euler-type methods for neutral stochastic delay differential equations (NSDDEs) using the discrete semimartingale convergence theorem.

It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions.

Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.