The paper focuses on the analysis of mean-square contractivity of the numerical dynamics arising from the application of θ-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 θ. A selection of numerical experiments complements the theoretical investigation.
Mean-Square Monotonicity Analysis of θ-Maruyama Methods
D'Ambrosio R.
2026-01-01
Abstract
The paper focuses on the analysis of mean-square contractivity of the numerical dynamics arising from the application of θ-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 θ. A selection of numerical experiments complements the theoretical investigation.File in questo prodotto:
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