This note extends and interprets a result of Saito and Mitsui [SIAM J. Numer. Anal., 33 (1996), pp. 2254–2267] for a method of Milstein. The result concerns mean-square stability on a stochastic differential equation test problem with multiplicative noise. The numerical method reduces to the Theta Method on deterministic problems. Saito and Mitsui showed that the deterministic A-stability prope...

k-fold cross validation is a popular practical method to get a good estimate of the error rate of a learning algorithm. Here, the set of examples is first partitioned into k equal-sized folds. Each fold acts as a test set for evaluating the hypothesis learned on the other k − 1 folds. The average error across the k hypotheses is used as an estimate of the error rate. Although widely used, espec...

Abstract The aim of this paper is the analysis exponential mean-square stability properties nonlinear stochastic linear multistep methods. In particular it known that, under certain hypothesis on drift and diffusion terms equation, contractivity visible: qualitative feature exact problem here analysed numerical perspective, to understand whether a method can provide an analogous behaviour which...