Stabilized methods for stiff stochastic systems

Stiff stochastic systems are usually solved numerically by (semi-)implicit methods, since explicit methods, such as the Euler-Maruyama scheme, face severe stepsize reductions. This comes at the cost of solving linear algebra systems at each step and can be expensive for large systems and complicated to implement for complex problems. In this Note, we introduce a new class of explicit methods for stochastic differential equations with multi-dimensional Wiener processes, with much better stability properties (in the mean square sense) than existing explicit methods. These new methods are as easy to implement as standard explicit schemes but much more efficient for handling stiff stochastic problems.