Stabilization of stochastic Runge-Kutta methods by TASE operators

We derive new classes of linearly implicit for systems of stochastic differential equations (SDEs) by employing the so-called Time-Accurate and highly-Stable Explicit (TASE) operators, introduced in the context of deterministic evolutive problems, in order to stabilize explicit numerical methods. In particular, we provide the TASE-based version of Euler-Maruyama method and some explicit stochastic Runge-Kutta methods for SDEs. Mean-square stability of TASE-based methods is analyzed and classes of mean-square A-stable methods are provided. A selection of numerical tests is reported, confirming the theoretical inspection.