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