Mean-Square Monotonicity Analysis of \(\theta \) -Maruyama Methods
摘要
The paper focuses on the analysis of mean-square contractivity of the numerical dynamics arising from the application of \(\theta \) -Maruyama methods to stochastic differential equations (SDEs) with linear affine drift and diffusion coefficients. We prove that the numerical deviation between two distinct solutions of the SDE is monotonically non-increasing under the same stepsize restrictions needed for mean-square stability or holds unconditionally for certain values of \(\theta \) . A selection of numerical experiments complements the theoretical investigation.