This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) with pathwise solutions that remain unconditionally bounded. This approach may offer modelling advantages in data assimilation, particularly when the signal or data is a realization of an SPDE or PDE with a monotonicity property.

翻译：本文将确定性框架下的强稳定性保持（SSP）概念扩展至随机情形，为具有无条件有界路径解的随机微分方程（SDE）和随机偏微分方程（SPDE）提供非线性稳定的数值解法。该方法在数据同化领域可能具有建模优势，尤其当信号或数据是具有单调性特征的SPDE或PDE的实现时。