Stability analysis of first order S-ROCK methods for stochastic differential equations with delays in the deterministic part.

An attempt to study the stability of first order S-ROCK methods applied to a stochastic differential equation with a delay in the deterministic part. The previous results for stochastic differential equations and delay differential equations are possible to be generalized since the splitting technique used in S-ROCKs for the stochastic part. Thus mean square stability notion is combined with P-stability for delay equations. Some choice of "optimal" damping coefficient of S-ROCKs is done. [ABSTRACT FROM AUTHOR]