Mean Square Polynomial Stability of Numerical Solutions to a Class of Stochastic Differential Equations

Mohammud Foondun; Wei Liu; Xuerong Mao

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arXiv · 1404.6073

Mean Square Polynomial Stability of Numerical Solutions to a Class of Stochastic Differential Equations

Mohammud Foondun·Wei Liu·Xuerong Mao

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Abstract

The exponential stability of numerical methods to stochastic differential equations (SDEs) has been widely studied. In contrast, there are relatively few works on polynomial stability of numerical methods. In this letter, we address the question of reproducing the polynomial decay of a class of SDEs using the Euler--Maruyama method and the backward Euler--Maruyama method. The key technical contribution is based on various estimates involving the gamma function.

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Mohammud Foondun, Wei Liu, Xuerong Mao. 2014-04-24. Mean Square Polynomial Stability of Numerical Solutions to a Class of Stochastic Differential Equations. https://arxiv.org/abs/1404.6073

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