A new one-parameter linear benchmark SDE is derived and used to demonstrate that lower-order explicit stochastic integrators can outperform higher-order ones in stability and accuracy over ranges of time-step sizes.
Asymptotical mean square stability of an equilibrium point of some linear numerical solutions with multiplicative noise.Stochastic Analysis and Applications, 14(3):313–353, 1996
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Numerical stability revisited: A family of benchmark problems for the analysis of explicit stochastic differential equation integrators
A new one-parameter linear benchmark SDE is derived and used to demonstrate that lower-order explicit stochastic integrators can outperform higher-order ones in stability and accuracy over ranges of time-step sizes.